Computers & Chemical Engineering最新文献

{"title":"Harnessing machine learning for water energy food nexus sustainability: developing a surrogate to multi-objective optimization","authors":"Fatima Mansour ,&nbsp;Michael Yehya ,&nbsp;Ali Ayoub ,&nbsp;Mahmoud Al-Hindi","doi":"10.1016/j.compchemeng.2025.109526","DOIUrl":"10.1016/j.compchemeng.2025.109526","url":null,"abstract":"<div><div>Integrated management of water, energy, and food resources is critical for achieving sustainability under rising environmental and demographic pressures, yet existing approaches either lack computational efficiency for real-time decision support or fail to capture the full complexity of sectoral interdependencies. This study presents a Water Energy Food Nexus Machine Learning based surrogate Model (WEFN-MLM). The key innovation lies in training a Random Forest algorithm on comprehensive multi-objective optimization outputs from thousands of diverse scenarios, enabling the model to learn complex nonlinear interdependencies and resource trade-offs without requiring explicit mathematical formulation of system relationships. A high-resolution Multi-Objective Optimization WEFN model (MOO-WEFN) is used to generate the training dataset, incorporating constraints for resource availability, caloric requirements, and environmental thresholds. The trained model demonstrates high predictive accuracy, with most output variables achieving R² values above 0.90 and cosine similarity scores near 1.0. Normalized absolute error analysis reveals strong performance consistency across system-level metrics, with select deviations in sector-specific outputs, particularly those highly sensitive to scenario dynamics or underrepresented in the training space. Compared to traditional optimization, the surrogate model achieves up to a 300,000-fold reduction in computation time. The surrogate model is validated using a randomly generated test set of scenarios that enables direct comparison between surrogate predictions and optimization results. The results highlight the model’s effectiveness for high-resolution nexus analysis and scenario exploration, while also acknowledging trade-offs between speed and precision. Findings underscore the importance of diverse training scenarios, careful application boundaries, and integration with policy processes to support resilient resource planning.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"206 ","pages":"Article 109526"},"PeriodicalIF":3.9,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797268","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cluster-based adaptive sampling methodology for systems modeling","authors":"Maaz Ahmad ,&nbsp;Yin Jun ,&nbsp;Marta Moreno-Benito ,&nbsp;Senthil Kumarasamy ,&nbsp;Harsha Nagesh Rao ,&nbsp;Jason Mustakis ,&nbsp;Iftekhar A Karimi","doi":"10.1016/j.compchemeng.2025.109527","DOIUrl":"10.1016/j.compchemeng.2025.109527","url":null,"abstract":"<div><div>Modeling real-world (experimental) or simulated (computational) systems using data-driven surrogate models involves selecting a sampling technique to generate the input-output data for training and selecting a surrogate form. In this work, we present a novel sampling technique, Cluster-based Adaptive Sampling, that generates training data smartly and adaptively for developing surrogate models over a given input domain. CAS iteratively clusters sampled points, defines Voronoi tessellation of cluster centroids, and approximates the tessellations using simple hypercubes. It then searches locally and globally over the domain at each iteration to identify nonlinear and under-explored regions respectively, where it samples two new points using a distance-based metric. CAS is agnostic to surrogate form and terminates automatically based on a surrogate quality metric. We assessed CAS against two existing sampling techniques on 40 diverse test functions using six surrogate forms. CAS outperformed both techniques in developing more accurate surrogates for a given computational effort and required lower computational effort for a specified accuracy across most test functions and forms. We highlight the practical applicability of CAS in modeling two pharmaceutical processes and showcase its superior performance over the two techniques.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"206 ","pages":"Article 109527"},"PeriodicalIF":3.9,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797269","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Evaluating the potential of plastic waste upcycling using thermochemical technologies: A case study in Spain","authors":"Roberto Cifuentes García ,&nbsp;Evan D. Erickson ,&nbsp;Mariano Martín ,&nbsp;Víctor M. Zavala","doi":"10.1016/j.compchemeng.2025.109524","DOIUrl":"10.1016/j.compchemeng.2025.109524","url":null,"abstract":"<div><div>A plastic waste upcycling value chain model has been applied to assess the potential of processing packaging waste in Spain using thermo-chemical technologies to produce low-density polyethylene (LDPE) and polypropylene (PP), which are highly valuable materials. The model projects an annual profit of 120.6 M$/yr, with a capital investment of 789.3 M$, generating 3285 jobs and contributing 65.5 M$/yr to Spain’s economy. The achieved circularity rate of the waste processing infrastructure exceeds 40 %, incorporating recycled HDPE and PET. Despite these advantages, regulatory gaps and market hesitancy toward recycled materials due to quality concerns hinder adoption. Additionally, economies of scale remain underutilized in Spain due to lower plastic waste collection levels compared to countries such as the United States. This network, while less profitable, is environmentally superior, yielding upcycled products with a Global Warming Potential 20–35 % lower than their virgin, fossil-fuel counterparts, confirming this as a viable and sustainable alternative.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"206 ","pages":"Article 109524"},"PeriodicalIF":3.9,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Multiperiod strategic planning of CO2 capture, transport, utilization and storage with multimodal transportation","authors":"Etienne Ayotte-Sauvé ,&nbsp;Robert Yandon ,&nbsp;Philippe Navarri ,&nbsp;Robert Symonds ,&nbsp;Robin Hughes ,&nbsp;Marzieh Shokrollahi ,&nbsp;Rebecca Modler","doi":"10.1016/j.compchemeng.2025.109525","DOIUrl":"10.1016/j.compchemeng.2025.109525","url":null,"abstract":"<div><div>To reach decarbonization objectives across the globe, scenario modelling studies indicate that carbon capture, utilization and storage (CCUS) will be essential. Planning CCUS deployment at the regional and national levels requires balancing complex trade-offs – such as when to phase-in infrastructure, where and how much CO₂ to capture, transport, utilize and store, as well as which policy measures to adopt.</div><div>We introduce a new multiperiod mixed-integer linear programming (MILP) model for the strategic planning of CCUS, with CO₂ transportation via pipelines, ships, trains and trucks. This model features the selection of capture units and their rates, geographically explicit pipeline network design (including reuse), vehicle fleet estimations, auxiliary transshipment processes, buffer storage, inland reservoirs as well as injection via ships in addition to offshore pipelines. To handle large scale case studies, a simple heuristic algorithm is presented.</div><div>The features of the proposed approach are demonstrated on an illustrative Eastern Canada case study involving pipelines, trains and ships. The influence of the temporal resolution chosen by the modeller on the quality of cost estimates and on calculation times is quantified. Compared to leading commercial algorithms, for large model instances the proposed heuristic is shown to produce better results (e.g. 10 % lower cost) with much less computation time (minutes instead of days). This widens the scope of potential use cases, including broader geographical regions and larger sensitivity studies. The annual evolution of an Eastern Canada CCUS value chain is analyzed, paying special attention to the interplay between CO₂ storage reservoir and transport constraints.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"206 ","pages":"Article 109525"},"PeriodicalIF":3.9,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797286","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robust control by applying reinforcement learning to adapt explicit model predictive control policies","authors":"Edward Hendrik Bras,&nbsp;Tobias Muller Louw,&nbsp;Steven Martin Bradshaw","doi":"10.1016/j.compchemeng.2025.109519","DOIUrl":"10.1016/j.compchemeng.2025.109519","url":null,"abstract":"<div><div>Reinforcement learning (RL) is a data-driven optimal control technique that has seen limited adoption in the process industries owing to high operational data requirements and the need to balance safe control with exploration. In contrast, Model Predictive Control (MPC) has been established as the benchmark method for optimal control in industrial applications but relies on a dynamic model of the controlled process. In this work, MPC is used as a starting point for online, continuing actor-critic RL applied to the simulated quadruple tank benchmark. Optimal control actions were precomputed as a function of the state space using the plant model, and a neural network was fitted to these data to generate an explicit MPC policy. Subsequently, this policy was adapted during closed-loop interaction of the RL agent with the (simulated) true plant, which exhibited different dynamics to the nominal plant model. The RL controller resolved the effects of plant-model mismatch on closed-loop control performance in the minimum-phase operating region by finding the optimal policy incrementally. In the non-minimum phase operating region, inverse response prevented the RL agent from operating effectively. From multivariable zero analysis, it was shown that process zeros very close to the origin or in the right half plane introduce a significant risk of closed-loop instability under RL control. This work’s findings show both the potential and limitations of RL by adapting precomputed optimal control policies and optimal cost functions (value functions) developed using non-linear MPC.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"206 ","pages":"Article 109519"},"PeriodicalIF":3.9,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797287","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A risk-aware LNG terminal scheduling digital twin based on deep reinforcement learning","authors":"Yee Hung Hong ,&nbsp;Jinglin Wang ,&nbsp;Chao Peng ,&nbsp;Jinsong Zhao","doi":"10.1016/j.compchemeng.2025.109520","DOIUrl":"10.1016/j.compchemeng.2025.109520","url":null,"abstract":"<div><div>At LNG receiving terminals, the daily send-out target fluctuates with seawater temperature, the accumulated runtime of parallel units, and planned start-up or shutdown sequences. Operators must still decide which pumps or vaporizers to activate under time pressure and incomplete information. In practice, these choices often rely on experience and short-term intuition rather than systematic evaluation, which can lead to uneven runtime distribution, maintenance bottlenecks, and unnecessary energy consumption. This study asks whether such human decision gaps can be reduced within the actual physical and organizational constraints of a working terminal. We develop RALT-DT, a risk-aware learning and control digital twin that integrates deep reinforcement learning with process-level physical models. The “risk-aware” feature is embodied in three aspects: (1) all policy decisions are constrained by explicit mass and heat-balance equations and safety interlocks, ensuring that the control actions remain within certified operating envelopes; (2) the learning reward explicitly penalizes excessive switching, uneven runtime dispersion, and deviations from preventive-maintenance requirements, treating long-term mechanical wear and operational stability as quantifiable risks; and (3) the system continuously monitors plant–model mismatch and adapts its confidence weighting, so that recommendations are moderated when uncertainty grows. To make the solution practical, the plant’s many operating devices are grouped into four core classes—low-pressure (LP) pumps, high-pressure (HP) pumps, open-rack vaporizers (ORV), and submerged-combustion vaporizers (SCV). A two-time-scale roster generator translates continuous policy outputs into binary start–stop schedules that meet maintenance lock-out and switch-inertia constraints. The resulting framework forms a closed learning loop that is both deterministic and interpretable. A one-month on-site shadow test was carried out, in which the algorithm’s decisions were compared with real operator schedules under live conditions. The digital twin achieved an average electrical energy reduction of 9.4 %, equivalent to a saving of about 754 MWh, without violating throughput or switching limits. When calibrated against plant telemetry and vendor performance curves, the model maintained consistent accuracy across varying load and temperature conditions. These results indicate that a physics-grounded and risk-aware learning framework can systematically enhance human decision quality in large-scale terminal operations. It converts intuition-driven scheduling into a reproducible and auditable policy that improves both electrical energy efficiency and asset reliability.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"206 ","pages":"Article 109520"},"PeriodicalIF":3.9,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797285","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Safe reinforcement learning via adaptive robust model predictive shielding","authors":"Hilde Gerold,&nbsp;Sergio Lucia","doi":"10.1016/j.compchemeng.2025.109521","DOIUrl":"10.1016/j.compchemeng.2025.109521","url":null,"abstract":"<div><div>Ensuring constraint satisfaction during the deployment of reinforcement learning (RL) controllers remains a key challenge for safety-critical systems. Model predictive shielding addresses this by verifying proposed actions through predictive models and replacing unsafe ones with a backup policy, but existing approaches can be overly conservative, computationally demanding, and difficult to design for nonlinear systems with uncertainty.</div><div>We propose Adaptive Robust Model Predictive Shielding to overcome these limitations. First, we employ an approximate robust nonlinear model predictive controller as the backup policy, trained offline from multi-stage robust model predictive control data. This robust model predictive shielding approach retains safety under uncertainty while enabling real-time applicability. Second, we introduce an adaptive safety parameter in the RL observation space, allowing the agent to dynamically adjust its conservativeness. Our adaptive model predictive shielding method thus enhances safety and adapts to current uncertainty levels while avoiding excessive conservatism. When deployed with a safe backup policy, adaptive robust model predictive shielding retains safety under uncertainty and reduces unnecessary backup interventions. Simulation results for a nonlinear continuous stirred tank reactor with parametric uncertainty show that the proposed adaptive robust model predictive shielding approach reduces interventions of backup policies while still guaranteeing safety. This framework can be especially beneficial for safe RL of chemical processes where a combination of safety guarantees, high performance, and real-time feasibility is critical.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"206 ","pages":"Article 109521"},"PeriodicalIF":3.9,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145749131","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Digital design of crystallization processes using statistical machine learning","authors":"Yash Barhate ,&nbsp;Yung Shun Kang ,&nbsp;Neda Nazemifard ,&nbsp;C․Benjamin Renner ,&nbsp;Yihui Yang ,&nbsp;Charles Papageorgiou ,&nbsp;Zoltan K. Nagy","doi":"10.1016/j.compchemeng.2025.109518","DOIUrl":"10.1016/j.compchemeng.2025.109518","url":null,"abstract":"<div><div>This study presents a generic statistical machine learning (ML)-driven modeling workflow for designing crystallization processes, serving as a practical alternative in situations where traditional mechanistic population-balance modeling approaches are impractical. Key highlights of the proposed workflow include synthetic data augmentation to reduce dependency on extensive experimental datasets; the incorporation of active learning strategies to iteratively suggest experimental conditions and refine experimental datasets; and the successful deployment of ML models within the Quality-by-Digital-Design (QbDD) framework. The effectiveness of the proposed approach is demonstrated through two case studies: (1) an <em>in-silico</em> study involving an agrochemical compound, and (2) an experimental case study with an industrial pharmaceutical compound. ML models trained in these scenarios achieved prediction errors below 10 % when predicting critical quality attributes (CQAs). These models subsequently enabled deterministic and probabilistic design space analyses, followed by model-based process optimization, and were confirmed through experimental validation. While the approaches are exemplified using crystallization processes, it provides a generic and systematic framework for the ML model, development applicable to reactions and other complex process systems.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"206 ","pages":"Article 109518"},"PeriodicalIF":3.9,"publicationDate":"2025-12-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797290","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A blockchain-based circular economy taxonomy model for secure & efficient toxic materials supply chain: A technology-based intervention and case study approach","authors":"Muhammad Shoaib ,&nbsp;Rongjian Yu ,&nbsp;Hassan Ali ,&nbsp;Amin Ullah Khan ,&nbsp;Ahmad Fraz","doi":"10.1016/j.compchemeng.2025.109517","DOIUrl":"10.1016/j.compchemeng.2025.109517","url":null,"abstract":"<div><div>Globalization makes the supply chain for toxic materials (TOM’s) complex and extensive, affecting their reliability and potentially causing disruptions across various operations. The toxic materials supply chain is a delicate industrial operation that requires significant attention. Integrating the circular economy and blockchain technology into the supply chain provides a substantial solution to this issue, as previous literature lacks a secure and efficient digital system. To achieve this, the state-of-the-art Technology-Based Intervention (TBI) was a cutting-edge methodology that often incorporated the latest technologies and tools, enabling more innovative research validation and efficient problem-solving. This study initially explored the hidden potential of blockchain and the detailed process of the circular supply chain, aiming to provide deep insights. Later, a blockchain-based circular-economy taxonomy model was proposed to enable a secure and efficient toxic-materials supply chain. This model comprises a blockchain design layout, with its key features implemented in the toxic materials circular supply chain (CSC) processes, aiming to achieve a secure and efficient supply chain by addressing key performance indicators (KPIs). Moreover, this paper examines YongTaiyun (永泰运) Chemical Logistics Co., Ltd. as a real-world case study to explore how conventional chemical logistics companies are transforming and upgrading in the digital era by integrating blockchain technology. This approach enables rigorous analysis of complex real-world phenomena, particularly the nexus of technology and industry practices. The results illustrate that blockchain mitigates toxic materials supply chain risks through digital automation and promotes zero waste by reusing, recycling, reprocessing, and remanufacturing used products. It enables governance agencies, traffic controllers, and transportation management to develop standards and policies to eliminate risks related to toxic chemicals, especially nuclear reactors, radiation leakage, irregularities, and illegal access, while providing secure and efficient documentation, handling, storage, and transportation systems. This research provides a comprehensive understanding and roadmap for academic scholars and researchers, aiming to help industrial practitioners, policymakers, and authorised agencies implement blockchain technology and develop informed rules on secure and efficient practices.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"207 ","pages":"Article 109517"},"PeriodicalIF":3.9,"publicationDate":"2025-12-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145923401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A cloud-enabled digital twin platform for upstream processing in biotechnology: Integrating CFD, compartmentalization, and reaction kinetics","authors":"Xiyan Li ,&nbsp;Sebastian L. Jensen ,&nbsp;Noah B. Christiansen ,&nbsp;Elham Ramin ,&nbsp;Johan le Nepvou de Carfort ,&nbsp;Johannes Schmölder ,&nbsp;Eric von Lieres ,&nbsp;Krist V. Gernaey","doi":"10.1016/j.compchemeng.2025.109488","DOIUrl":"10.1016/j.compchemeng.2025.109488","url":null,"abstract":"<div><div>Biotechnology process modeling has become an essential tool in both research and industrial settings, offering a cost-effective and efficient alternative to extensive physical experimentation. It enables the simulation and analysis of complex biological systems, supporting faster development cycles and better decision-making. To foster collaboration and knowledge sharing in this domain, we present an open source cloud-enabled platform for upstream biotechnology process modeling. The platform provides an integrated environment where users can combine computational fluid dynamics (CFD), compartmental models, and kinetic simulations within a unified and modular interface. Each component of the model operates independently, but can be seamlessly coupled through a standardized API. The system is designed to support both research and educational use cases, with an emphasis on accessibility, extensibility, and reproducibility. This paper outlines the platform architecture and implementation, highlights the technical challenges addressed in model integration, and discusses opportunities for future development. By lowering technical barriers and encouraging community-driven innovation, the platform aims to advance digital twin applications in biotechnology upstream processing.</div></div>","PeriodicalId":286,"journal":{"name":"Computers & Chemical Engineering","volume":"206 ","pages":"Article 109488"},"PeriodicalIF":3.9,"publicationDate":"2025-12-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836367","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}