Stochastic Operations Research Articles

Atom-Vacancy-Defect-Derived Electric Hysteresis Loops and Stochastic Low-Frequency Noises in Few-Atom Layer MoS2.

Atom-vacancy-defects present in various materials yield numerous interesting physical phenomena, even obstructing high performance in some cases. On the other hand, their valuable applications to novel devices, such as nitrogen vacancy centers in diamond for quantum bits, have gathered significant attention. In particular, these tendencies become more substantial in two-dimensional (2D) (atomically) thin van der Waals layers. However, correlations with various kinds of atom defects are still under exploration. Herein, we find the stochastic behaviors of large hysteresis loops with strong photoresponse in the static electrical properties in few-atom layer semiconductors, molybdenum disulfide (MoS2). The temperature dependence and transmission electron microscopy reveal that they arise from pairs of two neighboring in-plane S-vacancy defects, which predominantly present only around the interface at the MoS2 flake/substrate, with activation energies ∼0.35 eV. The low-frequency (f) (LF) noise measurements clarify a high f shift in the two 1/f2-dependent regimes, implying stochastic behaviors of electric charges through the S-vacancy pairs with high-speed charge(spin) transitions across low kinetic energy barriers between narrow discrete states. The shallow energy sates are formed from the highly uniform S-vacancy pairs interacting with Mo atoms, which act like quantum dots. The observed stochastic operation holds promise for various application, particularly for probabilistic neuromorphic computation in artificial intelligence.

Quantum Entanglement and Its Classification Protocols

Quantum entanglement has its own major role in quantum information theory. Its application in numerous areas namely quantum computing, quantum cryptography and quantum teleportation are proven vital and essential. Over the last decades, the interests in quantum entanglement have grown and significant progress in quantum computing has been revealed. However, the classification of entanglement was proved to be challenging especially in a higher qubit-dimensional system setting. In this review, indexed literature as the secondary resource was chosen by specific keywords from several database. In reference to the literatures review, there exists several entanglement classifications protocols that will be presented in this paper namely local unitary (LU), local operations and classical communication (LOCC), and stochastic local operations and classical communication (SLOCC). This study will offer a better understanding of quantum entanglement and the entanglement classification protocols.

COMPUTING THE DEGREE-4 INVARIANT POLYNOMIAL BASIS FOR 7 QUBITS

Understanding the complexity of entangled states within the context of SLOCC (stochastic local operations and classical communications) involving several number qubits is essential for advancing our knowledge of quantum systems. This complexity is often analyzed by classifying the states via local symmetry groups. Practically, tthe resulting classes can be distinguished using invariant polynomials, but the size of these polynomials grows rapidly. Hence, it is crucial to obtain the smallest possible invariants. In this short note, we compute the basis of invariant polynomials of 7 qubits of degree 4, which are the smallest degree invariants. We obtain these polynomials using the representation theory and algebraic combinatorics.

Distributionally Robust Optimization-Based Stochastic Operation Strategy of MVDC System in Distribution Networks

Distributionally Robust Optimization-Based Stochastic Operation Strategy of MVDC System in Distribution Networks

Phase sensitivity of entanglement in the Quantum Phase Estimation algorithm

We study entanglement in the steps before Quantum Fourier Transform (pre-QFT) part of the Quantum Phase Estimation and the Quantum Counting algorithms (QPEA—QCA) with the use of three entanglement detection tools. In particular we focus on the sensitivity of entanglement to the input value (the phase ϕ and the ratio of marked elements MN ) in some basic cases. One starts from numerical observations and deduce some general results in particular regarding the classes of entanglement. More precisely, when the second register of both algorithms (i.e. the register on which a specific unitary operator act, see section ) is initialized in the non-entangled superposition of two (separable) eigenvectors, one proves that the QPEA and QCA curves of entanglement evolution are the same up to a scalar multiplication of the parameter ϕ. One demonstrates that a local minimum is obtained and corresponds to an EPR (Einstein-Podolsky-Rosen) state and finally one proves that, up to Stochastic Local Operation and Classical Communication (SLOCC), all states, except for a few values of ϕ, are equivalent to the product of a separable state and a generalized GHZ (Greenberger-Horen-Zeilinger) state , i.e. GHZn+1=12(00...0+11...1) .

Stochastic Optimal Operation of SOP-Assisted Active Distribution Networks with High Penetration of Renewable Energy Sources

This paper introduces a mixed-integer convex model for optimizing the scheduling of soft open points (SOPs) integrated with energy storage (ES) in active distribution networks (ADNs) with high proportions of photovoltaic sources, designed to ensure zero risk of constraint violations. A stochastic optimization model for ADNs is proposed to maximize the benefits of SOPs while simultaneously minimizing system power losses, SOP power losses, voltage deviations, PV power curtailment, battery energy storage system (BESS) operation cost, and utility power purchase. Uncertainties in PV generation and load demand are considered by Monte Carlo simulation and k-means technologies. Finally, simulation cases from a 21-bus distribution network show that the curtailment of PV sources is minimized and the power fluctuations of the BESS are reduced in comparison to the case without SOP. Constraints in the nodal voltages, power outputs, energy balance, and power flow are all satisfied.

Human–Robot Collaborative Disassembly Line Balancing Problem With Stochastic Operation Time and a Solution via Multi-Objective Shuffled Frog Leaping Algorithm

Human–Robot Collaborative Disassembly Line Balancing Problem With Stochastic Operation Time and a Solution via Multi-Objective Shuffled Frog Leaping Algorithm

StocIPNet: A novel probabilistic interpretable network with affine-embedded reparameterization layer for high-dimensional stochastic inverse problems

The stochastic inverse problem (StocIP), which aims to align push-forward and observed output distributions by estimating probability distributions of unknown system inputs, often faces optimization challenges and the curse of dimensionality. A novel deep network called StocIPNet which comprises an affine-embedded reparameterization subnetwork (ReparNet) and a complex system metamodeling subnetwork (MetaNet) is proposed to alleviate these issues. The ReparNet subnetwork embeds the affine transformation to convert the statistical parameters of the physical random vector into learnable weights and biases, effectively implementing the reparameterization trick by separating random and deterministic elements in the stochastic sampling operation to preserve differentiability. In parallel, the MetaNet subnetwork offers a computationally efficient alternative to time-consuming forward solvers, facilitating the generation of push-forward distributions. The entire StocIPNet utilizes the kernel maximum mean discrepancy (MMD) as a distribution-free loss function, quantifying the discrepancy between push-forward and observed output distributions. By leveraging the ReparNet’s advantage of reformulating the sampling process as a differentiable transformation and combining two subnetworks seamlessly, the StocIP is reconfigured into a pure network training paradigm preserving differentiability perfectly, which allows for direct modeling and efficient inference of uncertainty within the network using automatic differentiation, backpropagation and gradient-based optimization methods, enabling ease of scaling to high-dimensional problems. The proposed framework has been theoretically demonstrated to be equivalent to the maximum likelihood method, ensuring its solid probabilistic interpretable foundation. The proposed framework is applied to perform stochastic model updating on a numerical and an experimental structure, which effectively demonstrates the framework’s remarkable effectiveness and high efficiency in treating high-dimensional StocIPs.

Comparison of data-driven stochastic window operation models for residential buildings

In residential buildings, window opening is typically one of the most significant parameters that affects indoor air temperature and thus the energy required for heating and cooling. While several field measurement campaigns have been undertaken, and datasets have been used to calibrate data-driven stochastic models based on different techniques, a critical comparison between these window operation models, analysing their suitability for building energy simulation, is needed. This study compares seven different modelling approaches including Gaussian distribution function, logistic regression, Markov chain, Markov-logit hybrid, classification tree, artificial neural network and random forest, trained and tested using measurements of 21 living rooms and 10 bedrooms from residential buildings located in Australian subtropical and temperate climates. Two types of modelling approaches were tested: individual, where each window operation was modelled individually, and cohort, where a common model was developed considering all the windows in the dataset. The stochastic nature of window opening was introduced to the models by Monte Carlo methods. True Positive Rate (TPR) and True Negative Rate (TNR), quantified using the Area Under Curve (AUC) method, were used to benchmark the performance of the different models. The classification trees and random forest were identified as more accurate methods (>0.74 median AUC) for cohort modelling, while artificial neural network and Markov-logit hybrid methods were identified as more accurate methods (>0.7 median AUC) for individual window operation modelling in building simulation applications.

Stochastic operation of Volt-VAr optimization and network reconfiguration-based energy management under different loading patterns

Stochastic operation of Volt-VAr optimization and network reconfiguration-based energy management under different loading patterns

Classification of large black holes

The black-hole--qubit correspondence has been proven to be ``useful for obtaining additional insight into one of the string black hole theory and quantum information theory by exploiting approaches of the other"[Phys. Rev. D 82, 026003 (2010)]. Though different classes of stringy black holes can be related to the well-known stochastic local operations and classical communication (SLOCC) entanglement classes of pure states, the string theory requires a more detailed classification than the SLOCC classification of three qubits. In this paper, we derive the entanglement family of three qubits under local unitary operations (LU), and use the black-hole--qubit correspondence to classify \textquotedblleft large\textquotedblright\ black holes into seven inequivalent families. In particular, we show that two black holes with 4 non-vanishing charges ($q_{0}$, $p^{1}$, $p^{2}$, and $p^{3}$) are LU equivalent if their difference is only in the signs of charges. Thus, the classification of black holes is independent of the signs of charges and is only related to the ratio of the absolute values of charges. This observation simplifies the classification task, as one would only need to consider either the classification of non-BPS black holes or the classification of BPS black holes, but not both. Moreover, through the LU classification, the physical basis for this black-hole--qubit correspondence can be observed, and a relation between the black-hole entropy and the von Neumann entanglement entropy is revealed. Therefore, the LU classification offers a more straightforward physical connection than the SLOCC classification. Based on the LU classification, we further study the properties of von Neumann entanglement entropy for each of the seven families, and find the black holes with the maximal von Neumann entanglement entropy.

Setting Plasma Immersion Ion Implantation of Ar+ Parameters towards Electroforming-Free and Self-Compliance HfO2-Based Memristive Structures.

Memristive structures are among the most promising options to be components of neuromorphic devices. However, the formation of HfO2-based devices in crossbar arrays requires considerable time since electroforming is a single stochastic operation. In this study, we investigate how Ar+ plasma immersion ion implantation (PI) affects the Pt/HfO2 (4 nm)/HfOXNY (3 nm)/TaN electroforming voltage. The advantage of PI is the simultaneous and uniform processing of the entire wafer. It is thought that Ar+ implantation causes defects to the oxide matrix, with the majority of the oxygen anions being shifted in the direction of the TaN electrode. We demonstrate that it is feasible to reduce the electroforming voltages from 7.1 V to values less than 3 V by carefully selecting the implantation energy. A considerable decrease in the electroforming voltage was achievable at an implantation energy that provided the dispersion of recoils over the whole thickness of the oxide without significantly affecting the HfOXNY/TaN interface. At the same time, Ar+ PI at higher and lower energies did not produce the same significant decrease in the electroforming voltage. It is also possible to obtain self-compliance of current in the structure during electroforming after PI with energy less than 2 keV.

Robust two‐level market coordinated transaction optimal model and benefit allocation strategy for a novel shared‐energy aggregator

AbstractShared‐energy storage (SES) can break the energy interaction barrier between the demand side and the supply side, which is becoming an option for improving the flexibility of energy systems. This study designed a novel structure for the shared‐energy aggregator (SEA), incorporating a microgrid (MG), prosumer and SES. Then, a two‐level market transaction optimization model for SEA, considering the robust stochastic optimization method, is proposed; namely, at the day‐ahead stage, a robust stochastic operation optimization model is constructed to achieve the dispatching plan from the demand side under the objective of achieving the minimum energy consumption cost for the prosumer, and at the real‐time market stage, a robust stochastic operation optimization model from the supply side is constructed to arrange the optimal dispatching strategy under the objective of the maximum aggregator benefits of MG and SES. Finally, an industrial park micro‐grid in Qinghai Province, China, is selected as an example for analysis.

Stochastic Flexible Resource Operations in Coordinated Green-Seaport Energy-Logistics Systems Using Constraint Generation Approach

The increasing penetration of renewable energy sources (RESs) in modern green seaports calls for more flexible management approaches that can minimize the daily seaport operation costs and RES curtailments. This paper establishes an optimal strategy in two-time intervals for flexible operations of energy storage systems and combined electric-thermal power demands of reefer containers in the coordinated green-seaport energy-logistics systems (ELS). For the day-ahead operation, a multi-stage stochastic optimization model is established to minimize the expected ELS operation cost according to the 24-hour-ahead forecasts. Uncertainties of RES power outputs, load demands, electricity prices, and ambient temperatures are considered in the optimization of day-ahead operation. For the intra-day operation, hydrogen, battery, and thermal storage systems as well as reefer containers operations are optimized based on the short-lead-time forecasts. Numerical simulations are carried out based on the Jurong seaport operation in Singapore to verify the effectiveness of the proposed optimal operation strategy for the coordinated green-seaport ELS. Simulation results reveal that the proposed strategy can achieve the lowest operation cost and the lowest RES curtailment in a green-seaport.

Deep learning the hierarchy of steering measurement settings of qubit-pair states

Quantum steering has attracted increasing research attention because of its fundamental importance, as well as its applications in quantum information science. Here we leverage the power of the deep learning model to infer the steerability of quantum states with specific numbers of measurement settings, which form a hierarchical structure. A computational protocol consisting of iterative tests is constructed to overcome the optimization, meanwhile, generating the necessary training data. According to the responses of the well-trained models to the different physics-driven features encoding the states to be recognized, we can numerically conclude that the most compact characterization of the Alice-to-Bob steerability is Alice’s regularly aligned steering ellipsoid; whereas Bob’s ellipsoid is irrelevant. We have also provided an explanation to this result with the one-way stochastic local operations and classical communication. Additionally, our approach is versatile in revealing further insights into the hierarchical structure of quantum steering and detecting the hidden steerability.

Optimal resource allocation and operation for smart energy hubs considering hydrogen storage systems and electric vehicles

Energy hubs (EHs) have substantially paved the way for the coordinated operation of various energy carriers, converters, and storage. However, the establishment of optimal planning and operation of the EH include several challenges, e.g., the stochastic nature of non-dispatchable generation assets, obtaining a satisfactory performance from the storage assets with reasonable energy and power density costs, and long-term load growth. Accordingly, this paper proposes a two-stage stochastic optimal resource allocation and operation approach for multiple smart energy hubs-based microgrids. The first stage optimizes the location of each EH and different assets' capacities. On the other hand, the second stage optimizes the charging/discharging rates of each asset and parking lot power. These microgrids combine renewable energy sources. Moreover, for research gap and unlike existing research, the cooperative operation of hybrid storage systems (i.e., solar-powered compressed air energy storage, hydrogen storage systems, battery energy storage systems, thermal energy storage systems) along with plug-in electric vehicles (PEV) has been investigated. Furthermore, annual load growth and price-based demand response (PBDR) are employed in this study. The simulation results demonstrate that the controlled charging/discharging of the PEVs reduces the total annualized cost by 5.49%, while the operation and emission costs are reduced by 21.3% and 19.86%, respectively. Furthermore, employing PBDR has led to a reduction of 10.1% in capital and operational costs.

Multiqubit entanglement due to quantum gravity

Quantum gravity between masses can produce entangled states in thought experiments. We extend the experiments to tripartite case and construct states equivalent to Greenberger- Horne-Zeilinger states and W states under stochastic local operations and classical communication. The entanglement relates to the evolution phases induced by gravitational interaction. When we involve more masses in the experiments, multipartite entangled states can be constructed in a similar way. We measure the degree of multipartite entanglement by calculating the geometric measure. We describe the relationship between geometric measure and the evolution phases. It helps searching out the states with robust entanglement.

Stochastic Operation of Multi-Terminal Soft Open Points in Distribution Networks with Distributionally Robust Chance-Constrained Optimization

Stochastic Operation of Multi-Terminal Soft Open Points in Distribution Networks with Distributionally Robust Chance-Constrained Optimization

Smart Grid Stochastic Optimization with Ant Colony-based Scenario Generation

This paper presents a stochastic optimization approach for the operational management of sustainable energy districts and polygeneration microgrids. Stochastic operation optimization allows for an uncertain approach to deal with imprecise variables. A new approach is here presented for generating scenarios based on Ant Colony Optimization (ACO) to assess the uncertainties related to inexact data, renewable energy sources and power demand. In fact, due to the uncertainties related to forecasting loads and renewables, it is necessary to analyze the probability of occurrence of the prediction and the different scenarios that could be faced. Then, based on the generated scenarios and probabilities, a scenario-based two-stage stochastic optimization approach has been formulated to optimize the operation strategies of the various technologies and solve the unit commitment problem under uncertainty. The developed models have been applied to the Savona Campus Smart Polygeneration Microgrid, and historical data from 2018 have been used.

Stochastic operation model for readiness assessment of small wind turbines based on Markov theory

AbstractWind energy is now one of the most important alternative sources of renewable energy. The development of wind power generation is a prerequisite to meet environmental and sustainable development requirements while achieving energy security goals. The condition for the effectiveness of the proper operation of a wind power plant is its ability to perform the intended functions, which can be expressed by the coefficient of technical readiness. This article presents an original analysis of the readiness of small wind turbines. As part of the research, an original stochastic operation model was developed based on the application of the Markov process theory. Based on the collected data, a 3‐state phase space of the studied process was identified. Various analyses were carried out to calculate the operating coefficients of wind power plants. The ergodic (boundary) probabilities were calculated using three methods. The conditional probabilities were then determined based on the initial distribution. The resulting readiness factors, not exceeding 30%, indicate the low operational efficiency of the small wind turbines in question. Furthermore, an analysis of the sensitivity of the performance factors was carried out for the analysed objects.