Transfer Operator Research Articles

Review of Outcomes After Peripheral Nerve Transfers for Motor Nerve Injury in the Upper Extremity

Background: Modern nerve-to-nerve transfers are a significant advancement in peripheral nerve surgery. Nerve transfers involve transferring donor nerves or branches to recipient nerves close to the motor end unit, leading to earlier reinnervation and preservation of the musculotendinous units in proximal nerve injuries. After nerve reinnervation, function may be superior to traditional tendon transfer techniques in terms of strength and independent motion. Nerve transfer surgery has emerged as a promising treatment option for many cases of nerve injury that were previously expected to result in poor outcomes, such as proximal injuries, long nerve gaps, or unavailability of the proximal injured segment. Methods: A review was conducted following the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. Publications that focused on upper extremity nerve transfers were included, and functional motor and sensory recovery was analyzed. Technique reports, case reports, brachial plexus injuries, and reports on multiple nerve injuries were excluded. Results: A total of 48 relevant articles were identified with search criteria, and we discuss functional outcomes on nerve transfers for ulnar nerve injury, musculocutaneous nerve injury, median nerve injury, and radial nerve injury that met inclusion criteria. Conclusions: Nerve transfers are an option for restoring hand and forearm function in patients with peripheral nerve injuries adversely affecting their ability to function. The literature demonstrates positive functional outcomes after nerve transfer operations, and thus, the utility and variations have increased. We aim to provide an overview of the outcomes of current nerve transfer techniques for ulnar, radial, median, and musculocutaneous acquired/traumatic mononeuropathies in the hand and upper extremity.

A feedback matrix based evolutionary multitasking algorithm for high-dimensional ROC convex hull maximization

Multi-objective evolutionary algorithms have shown their competitiveness in solving ROC convex hull maximization. However, due to “the curse of dimensionality”, few of them focus on high-dimensional ROCCH maximization. Therefore, in this paper, a feedback matrix (FM)-based evolutionary multitasking algorithm, termed as FM-EMTA, is proposed. In FM-EMTA, to tackle “the curse of dimensionality”, a feature importance based low-dimensional task construction strategy is designed to transform the high-dimensional ROCCH maximization task into several low-dimensional tasks. Then, each low-dimensional task evolves with a population. To ensure that the low-dimensional task achieves a better ROCCH, an FM-based evolutionary multitasking operator is proposed. Specifically, for each low-dimensional task i, the element FM(i,j) in feedback matrix is defined to measure the degree that the low-dimensional task j could assist task i. Based on it, an FM-based assisted task selection operator and an FM-based knowledge transfer operator are developed to constitute the evolutionary multitasking operator, with which the useful knowledge is transferred among the low-dimensional tasks. After the evolution, the best ROCCHs obtained by the low-dimensional tasks are combined together to achieve the final ROCCH on the original high-dimensional task. Experiments on twelve high-dimensional datasets with different characteristics demonstrate the superiority of the proposed FM-EMTA over the state-of-the-arts in terms of the area under ROCCH, the hypervolume indicator and the running time.

Dynamic modeling and robust control of a multi-cable payload transfer system for offshore cranes subjected to random waves and wind loads

The payload often experiences unpredictable motion due to the combined effects of random waves and wind loads, significantly impacting the safety and efficiency of offshore operations. To expand the effective working window for offshore transfer operations, this study introduces a multi-cable payload transfer system (MPTS). Using a 45-ton offshore crane mounted on a multipurpose vessel from COSCO Shipping Group as a prototype, this study establishes a dynamic model of MPTS, considering the effects of vessel motion, crane actions, and wind loads. The payload remains in an unstable state due to external disturbances. Additionally, variations in payload specifications and mass lead to considerable uncertainties in the dynamic parameters of MPTS. To address these uncertainties, a second-order linear observer is developed. Subsequently, an improved computed torque controller is proposed, and the boundedness of the tracking errors is proven using the Lyapunov theory. The transfer process is divided into three distinct phases: lifting, slewing, and lowering. The feasibility of the transfer scheme is verified through high-fidelity simulations and prototype experiments. This research provides a solid theoretical foundation for the subsequent engineering application of MPTS.

Discontinuities Cause Essential Spectrum on Surfaces

AbstractTwo-dimensional maps with discontinuities are considered. It is shown that, in the presence of discontinuities, the essential spectrum of the transfer operator is large whenever it acts on a Banach space with norm that is stronger than $$L^\infty $$ L ∞ or $$BV$$ BV . Three classes of examples are introduced and studied, both expanding and partially expanding. In two dimensions, there is complication due to the geometry of the discontinuities, an issue not present in the one-dimensional case and which is explored in this work.

An approach for thermal performance assessment and optimization design of energy diaphragm walls (EDWs) with seasonal thermal load via numerical modeling

The energy diaphragm wall (EDW) is a promising emerging technology for shallow geothermal energy utilization of existing buildings. However, analyzing the heat transfer characteristics of EDWs is a prerequisite and essential guarantee for rational heat transfer design and optimization. Generally, a single field or model test cannot fully consider and analyze the potential factors affecting the heat transfer characteristics. Therefore, this work uses numerical analysis methods to establish a 3D heat transfer numerical model of EDW suitable for the climatic and geological conditions and heat transfer requirements in Chongqing areas, China. The influencing parameters are divided into design, operating, and environmental aspects. A comprehensive analysis method has been developed that considers a range of indicators related to the temperature difference between the inlet and outlet, heat transfer efficiency, total heat transfer, and average daily heat transfer. The developed method also evaluates the significance of parameter effects based on transient and integrated heat transfer performance. The results show that the heat transfer fluid flow rate, operation mode, groundwater flow, excavation ratio and wall depth have the greatest impact on the thermal performance of the EDW, with a normalized influence degree NETotal of 1.0, 0.94, 0.80 and 0.77, respectively. Recommendations on the thermal conductivity of the concrete and pipe, pipe configuration, etc., and prospects for further research are also provided for the optimal design and thermal simulation optimization of energy diaphragm wall systems.

Two-Stage Optimization Model Based on Neo4j-Dueling Deep Q Network

To alleviate the power flow congestion in active distribution networks (ADNs), this paper proposes a two-stage load transfer optimization model based on Neo4j-Dueling DQN. First, the Neo4j graph model was established as the training environment for Dueling DQN. Meanwhile, the power supply paths from the congestion point to the power source point were obtained using the Cypher language built into Neo4j, forming a load transfer space that served as the action space. Secondly, based on various constraints in the load transfer process, a reward and penalty function was formulated to establish the Dueling DQN training model. Finally, according to the ε−greedy action selection strategy, actions were selected from the action space and interacted with the Neo4j environment, resulting in the optimal load transfer operation sequence. In this paper, Python was used as the programming language, TensorFlow open-source software library was used to form a deep reinforcement network, and Py2neo toolkit was used to complete the linkage between the python platform and Neo4j. We conducted experiments on a real 79-node system, using three power flow congestion scenarios for validation. Under the three power flow congestion scenarios, the time required to obtain the results was 2.87 s, 4.37 s and 3.45 s, respectively. For scenario 1 before and after load transfer, the line loss, voltage deviation and line load rate were reduced by about 56.0%, 76.0% and 55.7%, respectively. For scenario 2 before and after load transfer, the line loss, voltage deviation and line load rate were reduced by 41.7%, 72.9% and 56.7%, respectively. For scenario 3 before and after load transfer, the line loss, voltage deviation and line load rate were reduced by 13.6%, 47.1% and 37.7%, respectively. The experimental results show that the trained model can quickly and accurately derive the optimal load transfer operation sequence under different power flow congestion conditions, thereby validating the effectiveness of the proposed model.

Transient behavior of the DYNASWIRL® phase separator during cryogenics tank-to-tank transfer operations

In order to separate gas and liquid from a two-phase mixture in space or earth applications, one can generate a strong artificial acceleration field instead of relying on gravity. This can be achieved by generating a swirl flow in a separator. The DYNASWIRL® phase separator is such a passive device, which had been demonstrated in air/water mixtures in the laboratory and on five reduced gravity NASA parabolic flights. In this work, extensive laboratory testing and numerical simulations are conducted to demonstrate the validity of the DYNASWIRL for phase separation with cryogenics. Liquid nitrogen (LN2) is used for extensive testing involving unsteady tank-to-tank transfer with quenching of separator and piping, liquid boil-off and vaporization, phase separation and recovery. This paper describes the separator and testing setups used. It examines the effects of the liquid (water and LN2), geometric parameters, and their effects on the separation and on the pressure loss across the separator, and analyzes the flow dynamics of the gas removal process. Validated numerical simulations support the experimental results and help explain the effects of the design parameters on the results.

Translation of a story into Chilean Sign Language: productions by deaf co-teachers

IntroductionThe incorporation of narratives in Chilean Sign Language enriches classroom practices, preserving and transmitting Deaf culture. However, that within the Chilean educational context, the narratives used for instructing Deaf students are translations from written Spanish. This study aims to describe and analyze the narrative structure and the use of Highly Iconic Structures in these translations conducted by Deaf co-teachers into Chilean Sign Language.MethodThe research adopts a qualitative approach and a descriptive case study design, involving two deaf teachers from an Inclusive Education Program in a school. The data analyzed focus on the video-recorded LSCh translations of the short story “The Greedy Squirrel”. Manual annotations were made on the corpus gloss transcription to first segment by narrative structure for description and then to identify the transfer operations.ResultsThe co-teachers make variations to the narrative structure of the translated text and incorporate specific visual-gestural elements such as the change of narrator to first person; the 45% of the translation is composed of transfer operations.DiscussionThese findings suggest that the variations in structure and the new visual-gestural information provided by the co-teachers reflect their understanding and use of sign language narrative norms for translation. The use of transfer operations enhances the storytelling experience, although it cannot be conclusively stated how and why teachers decide to use them in translation. The results are limited, as they require comparison with other corpora on translations from written Spanish to LSCh and software-assisted analysis to standardize data, which implies further research on the topic. For now, it is essential that the time allocated to the preparation of educational materials in LSCh be more extensive and better planned.

The Magnitude Of The Informal Remittances Flow To Kenya: An Augmented Gravity Model Approach.

Background: In Kenya remittances are now a proper source of external finances. Kenya received $4.19 billion in form of diaspora remittances in year 2023. Over the years, remittances are proving to be more stable, well diversified and are promising more growth relative to foreign direct investments, official development assistance, private capital and exports. On the micro scale the remittances are helping achieve Kenya’s developmental goals of having a globally competitive human resource and an adequately and decently housed population as outlined in the country’s development blueprint - The Kenya Vision 2030. Though the remittances are these important, official remittance data in Kenya, as well as in many African countries, only include remittances sent through formal channels such as banks and Money transfer Operators. Remittances through the informal channels such as hawalas and hundis are not recorded. This means that the recorded remittances are grossly understated impeding the capacity of policy makers to design appropriate policies aimed at encouraging remittances. The study employed panel data analysis and a thought experiment on remittance data between 2013Q1 and 2022Q4. Through a thought experiment, the study asks what impact a reduction of the costs of sending remittances would have on remittances if the transaction costs were reduced to that of the informal channels of sending remittances. The analysis revealed that the size of the informal remittances in Kenya is between 20% and 26% of the formal remittances. On the determinants of remittance flows to Kenya, the study establishes that Kenyan migrants send more when the economic freedoms and economic conditions improve in their host nations but send less when economic freedoms back at home improve. Accurately measuring informal emittances in Kenya is vital for creating effective government policies. This data would reveal the true extent of remittances' impact on the economy, allowing policymakers to develop strategies that fully utilize their potential for development. By encouraging people to send money through official channels, the government can increase tax income, improve access to financial services, and better monitor these transactions. Additionally, understanding the size of informal remittances is essential for combating financial crimes like money laundering and ensuring that resources are used efficiently

Informal Foreign Currency Market Rate Coordination and Remittance Flows

ABSTRACT An unintended consequence of remittance flows to economically troubled countries may be the exacerbation of parallel foreign currency market activities. Studying clandestine markets is often hobbled by a lack of data on informal market coordination mechanisms. This paper examines the impact of the sudden cessation of an informal foreign currency exchange reference rate in Zimbabwe on inward remittance flows and public attention to money transfer operators. While the reference rate existed, there was bi-directional feedback between black market currency rates and retail diaspora remittance flows, but not with the flows of non-governmental organizations (NGOs). The abolition of the informal reference rate did not stall retail diaspora remittance flows. NGO remittances reacted negatively to the ban, suggesting concerns with government policy. Online attention on money transfer operators increased after the reference rate’s cessation suggesting remitters shifted to formal channels. Accordingly, remittance costs reduced significantly.

Prediction of human error probability in helicopter to ship transfer operation under an evidential reasoning extended CREAM approach.

Although the helicopter to ship transfer operation is rarely applied in ports around the world, some of the hub ports have encouraged it. The operational process poses challenges to safety due to the nature of the work to be completed by the ship crew. This article performs a systematic human error prediction to ensure safe helicopter to ship transfer operations under different circumstances since the human factor is becoming a significant contributor to maritime accidents. To accomplish this, the article addresses a cognitive reliability and error analysis method (CREAM) under the evidential reasoning (ER) approach. In the proposed approach, the CREAM provides a comprehensive human error prediction tool and ER is capable of supporting experts' judgment in decision-making. The findings of the research show that 'Secure the loose objects within or adjacent to the operating area' poses a high human error probability (4.50E-02) during helicopter to ship transfer operations.

Attention-Guided and Topology-Enhanced Shift Graph Convolutional Network for Skeleton-Based Action Recognition

Graph Convolutional Networks (GCNs) have emerged as a game-changer in skeleton-based action recognition. However, most previous works are resource-heavy, with large FLoating-number OPerations (FLOPs) limiting the model’s potential. A recent work involving shift operators to GCN (Shift-GCN) has successfully introduced a lightweight GCN, but there is still a performance gap compared to previous results. Inspired by Shift-GCN, we propose an innovative and novel model named attention-guided and topology-enhanced shift graph convolutional network (AT-Shift-GCN), which continues the lightweight benchmark and provides a more powerful performance. We employ a topological transfer operation to aggregate the information flow of different channels and extract spatial information. In addition, to extract temporal information across scales, we apply attention to interacting with shift convolution kernels of different lengths. Furthermore, we integrate an ultralight spatiotemporal attention module to fuse spatiotemporal details and provide robust neighborhood representation. In summary, AT-Shift-GCN is a breakthrough in skeleton-based action recognition that provides a lightweight model with enhanced performance on three datasets.

Intelligent Analysis of Avian Influenza Virus Biomarkers Based on Chemiluminescence Resonance Energy Transfer and DNA Logic Analysis.

A one-step logical analysis of multiple targets remains challenging. Herein, we report a one-pot and intelligent DNA logical analysis platform for the diagnosis of avian influenza virus (AIV) biomarkers based on chemiluminescence resonance energy transfer (CRET) and logic operations. On the surface of Lum/PEI/CaCO3 microparticles, the excited state of luminol underwent CRET with fluorescein isothiocyanate or rhodamine B isothiocyanate, producing three well-separated light emissions at 425, 530, and 590 nm, respectively. Taking advantage of the close distance between fluorophores aligned by the catalytic hairpin assembly reaction, the CRET efficiency was greatly enhanced (53.1%). H1N1, H7N9, and H5N1 were detected with limits of detection values as low as 15, 34, and 58 pM, respectively. Three-input logic circuits were simultaneously conducted on the surface of Lum/PEI/CaCO3 microparticles, enabling the rapid and accurate discrimination of multiple AIV biomarkers in one solution. In terms of peak positions and the normalized value of the total peak intensity, three biomarkers can be simultaneously discriminated without any other complex operations. In summary, the CRET-based multiple analytical assay was developed as an intelligent biosensor for identifying AIV biomarkers, having promising application prospects in the field of multiple analysis and precise disease diagnosis.

Numerical study of fluid flow and entropy optimization subject to second order slip condition across a permeable curved surface

The entropy generation analysis has great significance in the industrial sectors with heat transmission and fluid flows, for evaluating the irreversibility aspect of a system in heat transfer operations. The numerical simulation of entropy generation and the nanofluid flow across a permeable curved surface subject to cross-diffusion and irregular heat source/sink is reported in the current investigation. The thermodynamics 2nd law is used to simulate the entropy optimization. The flow phenomena are mathematically described by partial differential equations (PDEs), which are derived in a curvilinear coordinate system. The system of ODEs (ordinary differential equations) is derived by using the similarity conversion, which is further numerically calculated through the parametric continuation method (PCM) using MATLAB software. The results reveal that the velocity slip and curvature parameters improve the velocity profile whereas the inverse effect is observed against the surface permeability parameter. It can also be noticed that the entropy optimization enhances with the variation in Brinkman number and temperature ratio parameter. The impact of Schmidt number and chemical reaction decline the mass transmission ratio.

Hybrid of non-dominated sorting genetic algorithm II and invasive weed optimization for fan duct surface heat exchanger configuration optimization design

In this research, configuration optimization was conducted for FDSHX (fan duct surface heat exchanger) that is a new type of heat exchanger adopted in aero-engine heat management in recent years. Firstly, a method of Taguchi-ANFIS (Taguchi-Adaptive Neuro-Fuzzy Inference System), which can reduce training data volume utilizing orthogonal experimental matrix, was proposed to construct a rapid response mathematical model between three configuration parameters, including fin pitch, fin thickness, and oil passages number, and two design indicators, including heat transfer capacity and operating weight, based on the data prepared by an experimental validated FDSHX heat transfer capacity calculation method using heat transfer unit simulation. Secondly, a hybrid method of NSGA II-IWO (Non-dominated Sorting Genetic Algorithm II-Invasive Weed Optimization), which can simultaneously obtain the strong abilities of exploration and escaping from trap into local optima, was proposed to drive the constructed response mathematical model to enhance heat transfer through adjusting the three configuration parameters. Optimization comparison was performed between NSGA II-IWO and four classic optimization algorithms including GA (Genetic Algorithm), IWO (Invasive Weed Optimization), CA (Cultural Algorithm), and HS (Harmony Search). This research provides an integrated solution to help mechanical engineers improve the applicability and reasonableness of FDSHX design.

The qP- and qSV-wave separation in 2D vertically transversely isotropic media and their applications in elastic reverse time migration

Compressional and shear wave separation is an important step in anisotropic elastic reverse time migration (ERTM). With separated wavefields, we can generate images between different wave types and reveal more subsurface physical properties, as well as remove unwanted crosstalk and improve image quality. Traditional Helmholtz decomposition based on divergence and curl operations for isotropic media cannot be directly extended to vertically transversely isotropic (VTI) media. Wave-mode separation methods, similar to the nonstationary spatial filter and Poynting vector, cannot preserve the phase and amplitude information of the original coupled wavefield, thus limiting their application in ERTM. Currently, the anisotropic wavefield decomposition methods include the wavenumber-domain approach, the low-rank approximation, and other separation approaches based on different approximations, e.g., weak or elliptical anisotropy. These methods are either computationally intensive or involve large separation errors, especially in models with strong heterogeneities and anisotropy. The VTI wavefield separation operator is essentially defined in a mixed space-wavenumber domain. We introduce scalar operators to transfer operations from this mixed space-wavenumber domain to the space domain. The local wave propagation direction in the scalar operators is estimated using the Poynting vector, which is highly computationally efficient in the space domain. When we apply the wave separation method to ERTM, we not only obtain the vectorized qP and qSV waves but also retrieve the scalar qP wavefield. The scalar and vector wavefields preserve the amplitude and phase information in the original coupled wavefield. For anisotropic ERTM, we suggest using the scalar imaging condition to generate the PP image and the magnitude- and sign-based vector imaging condition to produce the PS image, both having higher image accuracy than the dot-product imaging condition. Numerical examples are used to validate our anisotropic wavefield separation method and the related ERTM workflow.

Level-2 IFS thermodynamic formalism: Gibbs probabilities in the space of probabilities and the push-forward map

We will denote by M the space of Borel probabilities on the symbolic space Ω = { 1 , 2 ⋯ , m } N . M is equipped Monge–Kantorovich metric. We consider here the push-forward map T : M → M as a dynamical system. The space of Borel probabilities on M is denoted by M . Given a continuous function A : M → R , an a priori probability Π 0 on M , and a certain convolution operation acting on pairs of probabilities on M , we define an associated Level-2 IFS Ruelle operator. We show the existence of an eigenfunction and an eigenprobability Π ^ ∈ M for such an operator. Under a normalization condition for A, we show the existence of some T -invariant probabilities Π ^ ∈ M . We are able to define the variational entropy of such Π ^ and a related maximization pressure problem associated to A. In some particular examples, we show how to get eigenprobabilities solutions on M for the Level-2 Thermodynamic Formalism problem from eigenprobabilities on M for the classical (Level-1) Thermodynamic Formalism; this shows that our approach is a natural generalization of the classic case.

Thermodynamics of chaotic relaxation processes.

The established thermodynamic formalism of chaotic dynamics, valid at statistical equilibrium, is here generalized to systems out of equilibrium that have yet to relax to a steady state. A relation between information, escape rate, and the phase-space average of an integrated observable (e.g., Lyapunov exponent, diffusion coefficient) is obtained for finite time. Most notably, the thermodynamic treatment may predict the phase-space profile of any integrated observable for finite time, from the leading and subleading eigenfunctions of the Perron-Frobenius or Koopman transfer operator. Examples of that equivalence are shown, and the theory is tested analytically on the Bernoulli map while numerically on the perturbed cat map, the Hénon map, and the Ikeda map, all paradigms of chaos.

C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*$$\\end{document}-Algebras Associated to Transfer Operators for Countable-to-One Maps

Our initial data is a transfer operator L for a continuous, countable-to-one map φ:Δ→X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi :\\Delta \\rightarrow X$$\\end{document} defined on an open subset of a locally compact Hausdorff space X. Then L may be identified with a ‘potential’, i.e. a map ϱ:Δ→X\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varrho :\\Delta \\rightarrow X$$\\end{document} that need not be continuous unless φ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\varphi $$\\end{document} is a local homeomorphism. We define the crossed product C0(X)⋊L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0(X)\\rtimes L$$\\end{document} as a universal C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*$$\\end{document}-algebra with explicit generators and relations, and give an explicit faithful representation of C0(X)⋊L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0(X)\\rtimes L$$\\end{document} under which it is generated by weighted composition operators. We explain its relationship with Exel–Royer’s crossed products, quiver C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*$$\\end{document}-algebras of Muhly and Tomforde, C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*$$\\end{document}-algebras associated to complex or self-similar dynamics by Kajiwara and Watatani, and groupoid C∗\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C^*$$\\end{document}-algebras associated to Deaconu–Renault groupoids. We describe spectra of core subalgebras of C0(X)⋊L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0(X)\\rtimes L$$\\end{document}, prove uniqueness theorems for C0(X)⋊L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0(X)\\rtimes L$$\\end{document} and characterize simplicity of C0(X)⋊L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0(X)\\rtimes L$$\\end{document}. We give efficient criteria for C0(X)⋊L\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$C_0(X)\\rtimes L$$\\end{document} to be purely infinite simple and in particular a Kirchberg algebra.

Multi-Task Multi-Objective Evolutionary Search Based on Deep Reinforcement Learning for Multi-Objective Vehicle Routing Problems with Time Windows

The vehicle routing problem with time windows (VRPTW) is a widely studied combinatorial optimization problem in supply chains and logistics within the last decade. Recent research has explored the potential of deep reinforcement learning (DRL) as a promising solution for the VRPTW. However, the challenge of addressing the VRPTW with many conflicting objectives (MOVRPTW) still remains for DRL. The MOVRPTW considers five conflicting objectives simultaneously: minimizing the number of vehicles required, the total travel distance, the travel time of the longest route, the total waiting time for early arrivals, and the total delay time for late arrivals. To tackle the MOVRPTW, this study introduces the MTMO/DRP-AT, a multi-task multi-objective evolutionary search algorithm, by making full use of both DRL and the multitasking mechanism. In the MTMO/DRL-AT, a two-objective MOVRPTW is constructed as an assisted task, with the objectives being to minimize the total travel distance and the travel time of the longest route. Both the main task and the assisted task are simultaneously solved in a multitasking scenario. Each task is decomposed into scalar optimization subproblems, which are then solved by an attention model trained using DRL. The outputs of these trained models serve as the initial solutions for the MTMO/DRL-AT. Subsequently, the proposed algorithm incorporates knowledge transfer and multiple local search operators to further enhance the quality of these promising solutions. The simulation results on real-world benchmarks highlight the superior performance of the MTMO/DRL-AT compared to several other algorithms in solving the MOVRPTW.