从故事生成程序到大语言模型:人工智能编剧创作的历史与实践

人工智能生成内容(AI Generated Content,简称AIGC)电影包括内涵丰富的多种维度,从编剧角度可以分为AI生成故事(AI Generated Storyline,简称AIGSL)与AI生成剧本(AI Generated Screenplay,简称AIGSP)。AIGSL研究始于20世纪60年代初,按照创作模式可以分为基于结构模型的故事生成、基于规则的故事生成和基于机器学习的故事生成三类程序。2022年底以来,以Chat GPT为代表的大语言模型将AIGC的内容从简单的AIGSL拓展到了AIGSP领域,同时催生了基于大语言模型的专用故事与剧本生成工具。大语言模型的故事和剧本生产存在事实错误、陈词滥调以及主观偏见等天然缺陷,但AIGSL与AIGSP已经开始实现产业化。目前的人工智能编剧创作绝大多数并不完全由AI创作,属于弱人工智能领域。中国电影工作者与软件工程师有必要利用机器学习等AI技术,学习中国传统叙事文本并总结其叙事风格,为具有中国叙事特色的编剧创作提供智能助力。

Hepatic arterial infusion chemotherapy with anti-angiogenesis agents and immune checkpoint inhibitors for unresectable hepatocellular carcinoma and meta-analysis

BACKGROUND Hepatic arterial infusion chemotherapy(HAIC)has been proven to be an ideal choice for treating unresectable hepatocellular carcinoma(uHCC).HAIC-based treatment showed great potential for treating uHCC.However,large-scale studies on HAIC-based treatments and meta-analyses of first-line treatments for uHCC are lacking.AIM To investigate better first-line treatment options for uHCC and to assess the safety and efficacy of HAIC combined with angiogenesis inhibitors,programmed cell death of protein 1(PD-1)and its ligand(PD-L1)blockers(triple therapy)under real-world conditions.METHODS Several electronic databases were searched to identify eligible randomized controlled trials for this meta-analysis.Study-level pooled analyses of hazard ratios(HRs)and odds ratios(ORs)were performed.This was a retrospective single-center study involving 442 patients with uHCC who received triple therapy or angiogenesis inhibitors plus PD-1/PD-L1 blockades(AIPB)at Sun Yat-sen University Cancer Center from January 2018 to April 2023.Propensity score matching(PSM)was performed to balance the bias between the groups.The Kaplan-Meier method and cox regression were used to analyse the survival data,and the log-rank test was used to compare the suvival time between the groups.RESULTS A total of 13 randomized controlled trials were included.HAIC alone and in combination with sorafenib were found to be effective treatments(P values for ORs:HAIC,0.95;for HRs:HAIC+sorafenib,0.04).After PSM,176 HCC patients were included in the analysis.The triple therapy group(n=88)had a longer median overall survival than the AIPB group(n=88)(31.6 months vs 14.6 months,P<0.001)and a greater incidence of adverse events(94.3%vs 75.4%,P<0.001).CONCLUSION This meta-analysis suggests that HAIC-based treatments are likely to be the best choice for uHCC.Our findings confirm that triple therapy is more effective for uHCC patients than AIPB.

Recent Progress in Reinforcement Learning and Adaptive Dynamic Programming for Advanced Control Applications

Reinforcement learning(RL) has roots in dynamic programming and it is called adaptive/approximate dynamic programming(ADP) within the control community. This paper reviews recent developments in ADP along with RL and its applications to various advanced control fields. First, the background of the development of ADP is described, emphasizing the significance of regulation and tracking control problems. Some effective offline and online algorithms for ADP/adaptive critic control are displayed, where the main results towards discrete-time systems and continuous-time systems are surveyed, respectively.Then, the research progress on adaptive critic control based on the event-triggered framework and under uncertain environment is discussed, respectively, where event-based design, robust stabilization, and game design are reviewed. Moreover, the extensions of ADP for addressing control problems under complex environment attract enormous attention. The ADP architecture is revisited under the perspective of data-driven and RL frameworks,showing how they promote ADP formulation significantly.Finally, several typical control applications with respect to RL and ADP are summarized, particularly in the fields of wastewater treatment processes and power systems, followed by some general prospects for future research. Overall, the comprehensive survey on ADP and RL for advanced control applications has d emonstrated its remarkable potential within the artificial intelligence era. In addition, it also plays a vital role in promoting environmental protection and industrial intelligence.

Efficacy and predictive factors of transarterial chemoembolization combined with lenvatinib plus programmed cell death protein-1 inhibition for unresectable hepatocellular carcinoma

BACKGROUND The efficacy and safety of transarterial chemoembolization(TACE)combined with lenvatinib plus programmed cell death protein-1(PD-1)for unresectable hepato-cellular carcinoma(HCC)have rarely been evaluated and it is unknown which factors are related to efficacy.AIM To evaluate the efficacy and independent predictive factors of TACE combined with lenvatinib plus PD-1 inhibitors for unresectable HCC.METHODS This study retrospectively enrolled patients with unresectable HCC who received TACE/lenvatinib/PD-1 treatment between March 2019 and April 2022.Overall survival(OS)and progression-free survival(PFS)were determined.The objective response rate(ORR)and disease control rate(DCR)were evaluated in accordance with the modified Response Evaluation Criteria in Solid Tumors.Additionally,the prognostic factors affecting the clinical outcome were assessed.RESULTS One hundred and two patients were enrolled with a median follow-up duration of 12.63 months.The median OS was 26.43 months(95%CI:17.00-35.87),and the median PFS was 10.07 months(95%CI:8.50-11.65).The ORR and DCR were 61.76%and 81.37%,respectively.The patients with Barcelona Clinic Liver Cancer Classification(BCLC)B stage,early neutrophil-to-lymphocyte ratio(NLR)response(decrease),or early alpha-fetoprotein(AFP)response(decrease>20%)had superior OS and PFS than their counterparts.CONCLUSION This study showed that TACE/lenvatinib/PD-1 treatment was well tolerated with encouraging efficacy in patients with unresectable HCC.The patients with BCLC B-stage disease with early NLR response(decrease)and early AFP response(decrease>20%)may achieve better clinical outcomes with this triple therapy.

Rehabilitation care for pain in elderly knee replacement patients

BACKGROUND Total knee arthroplasty(TKA)is recognized as the most effective surgical intervention for relieving pain and improving joint mobility and deformity in patients with knee osteoarthritis and other synovial diseases.The application of accelerated postoperative rehabilitation(enhanced recovery after surgery)has demonstrated its efficacy in improving patient outcomes,and early postoperative joint function exercise has become a key prognostic factor in knee replacement.The unexpected appearance of limb pain and swelling hindered the patient’s tendency for early mobilization,leading in prolonged hospitalization,delayed functional recovery and negative psychological responses.A retrospective analysis was conducted on a cohort of 116 patients who under-went TKA at our hospital between July 2019 and July 2021.The patients were divided into two groups:A control group(n=58)receiving programmatic nur-sing,and an observed group(n=58)receiving programmed nursing combined with a collaborative nursing model.A pain management team consisting of attending physicians,head nurses,and responsible nurses was established.Outcome measures included visual analogue scale(VAS)scores,activities of daily living(ADL)scale scores,and functional scores.The ADL scores of patients in both groups exhibited a continuous increase.However,there was no statistically significant difference in the ADL scores between the two groups at 48 h and the 7th d post-surgery(P>0.05).Upon reexamination at the 3rd mo,the observation group demonstrated higher ADL scores compared to the control group(67.48±14.69 vs 59.40±16.06,P<0.05).The VAS scores of both groups significantly decreased,with no significant difference observed between the groups at each time point(P>0.05).The functional status of patients in both groups exhibited a gradual increase prior to intervention and at the 1st,2nd,and 3rd month following discharge(P<0.05).There was no statistically significant difference in knee joint function scores between the two groups at the 1st month after discharge(47.52 vs 45.81,P>0.05).However,the knee joint function scores of patients in the observation group were significantly higher than those in the control group at the 2nd(59.38 vs 53.19,P<0.05)and 3rd month(71.92 vs 64.34,P<0.05)following discharge.CONCLUSION The utilization of programmed pain nursing in conjunction with collaborative nursing for out-of-hospital care of TKA patients has demonstrated favorable outcomes,encompassing pain reduction,enhanced prognosis,and improved nursing quality for patients.

Crosstalk among mitophagy,pyroptosis,ferroptosis,and necroptosis in central nervous system injuries

Central nervous system injuries have a high rate of resulting in disability and mortality;however,at present,effective treatments are lacking.Programmed cell death,which is a genetically determined fo rm of active and ordered cell death with many types,has recently attra cted increasing attention due to its functions in determining the fate of cell survival.A growing number of studies have suggested that programmed cell death is involved in central nervous system injuries and plays an important role in the progression of brain damage.In this review,we provide an ove rview of the role of programmed cell death in central nervous system injuries,including the pathways involved in mitophagy,pyroptosis,ferroptosis,and necroptosis,and the underlying mechanisms by which mitophagy regulates pyroptosis,ferroptosis,and necro ptosis.We also discuss the new direction of therapeutic strategies to rgeting mitophagy for the treatment of central nervous system injuries,with the aim to determine the connection between programmed cell death and central nervous system injuries and to identify new therapies to modulate programmed cell death following central nervous system injury.In conclusion,based on these properties and effects,interventions targeting programmed cell death could be developed as potential therapeutic agents for central nervous system injury patients.

An integrated MINLP model for multi-party coordination in downstream oil supply chain

Cooperation among enterprises can bring overall and individual performance improvement,and a smooth coordination method is indispensable.However,due to the lack of customized coordination methods,cooperation in the downstream oil supply chain cannot be carried out smoothly.This paper intends to propose a multi-party coordination method to promote cooperation between oil shippers and pipeline operator by optimizing oil transportation,oil substitution and pipeline pricing schemes.An integrated game-theoretic modeling and analysis approach is developed to characterize the operation behaviors of all stakeholders in the downstream oil supply chain.The proposed mixed integer nonlinear programming model constrains supply and demand capacity,transportation routes,oil substitution rules and pipeline freight levels.Logarithm transformation and price discretization are introduced for model linear approximation.Simulation experiments are carried out in the oil distribution system in South China.The results show that compared to the business-as-usual scheme,the new scheme saves transportation cost by 3.48%,increases pipeline turnover by 5.7%,and reduces energy consumption and emissions by 7.66%and 6.77%.It is proved that the proposed method improves the revenue of the whole system,achieves fair revenue distribution,and also improves the energy and environmental benefits of the oil supply chain.

Effect of eccentric and inclined loading on the bearing capacity of strip footing placed on rock mass

This paper deals with the bearing capacity determination of strip footing on a rock mass in hilly area by considering the influence of inclined and eccentric loading. Applying the generalized HoekBrown failure criterion, the failure behavior of the rock mass is modeled with the help of the power cone programming in the lower bound finite element limit analysis framework. Using bearing capacity factor(Ns), the change in bearing capacity of the strip footing due to the occurrence of eccentrically inclined loading is presented. The variations of the magnitude of Ns are obtained by examining the effects of the Hoek-Brown rock mass strength parameters(uniaxial compressive strength(sci), disturbance factor(D), rock parameter(mi), and Geological Strength Index(GSI)) in the presence of different magnitudes of eccentricity(e) and inclination angle(λ) with respect to the vertical plane, and presented as design charts. Both the inclined loading modes, i.e., inclination towards the center of strip footing(+λ) and inclination away from the center of strip footing(-λ), are adopted to perform the investigation. In addition, the correlation between the input parameters and the corresponding output is developed by utilizing the artificial neural network(ANN). Additionally, from sensitivity analysis, it is observed that inclination angle(λ) is the most sensitive parameter. For practicing engineers, the obtained design equation and design charts can be beneficial to understand the bearing capacity variation in the existence of eccentrically inclined loading in mountain areas.

Smart prediction of liquefaction-induced lateral spreading

The prediction of liquefaction-induced lateral spreading/displacement(Dh)is a challenging task for civil/geotechnical engineers.In this study,a new approach is proposed to predict Dh using gene expression programming(GEP).Based on statistical reasoning,individual models were developed for two topographies:free-face and gently sloping ground.Along with a comparison with conventional approaches for predicting the Dh,four additional regression-based soft computing models,i.e.Gaussian process regression(GPR),relevance vector machine(RVM),sequential minimal optimization regression(SMOR),and M5-tree,were developed and compared with the GEP model.The results indicate that the GEP models predict Dh with less bias,as evidenced by the root mean square error(RMSE)and mean absolute error(MAE)for training(i.e.1.092 and 0.815;and 0.643 and 0.526)and for testing(i.e.0.89 and 0.705;and 0.773 and 0.573)in free-face and gently sloping ground topographies,respectively.The overall performance for the free-face topology was ranked as follows:GEP>RVM>M5-tree>GPR>SMOR,with a total score of 40,32,24,15,and 10,respectively.For the gently sloping condition,the performance was ranked as follows:GEP>RVM>GPR>M5-tree>SMOR with a total score of 40,32,21,19,and 8,respectively.Finally,the results of the sensitivity analysis showed that for both free-face and gently sloping ground,the liquefiable layer thickness(T_(15))was the major parameter with percentage deterioration(%D)value of 99.15 and 90.72,respectively.

Development of small molecule drugs targeting immune checkpoints

Immune checkpoint inhibitors(ICIs)are used to relieve and refuel anti-tumor immunity by blocking the interaction,transcription,and translation of co-inhibitory immune checkpoints or degrading co-inhibitory immune checkpoints.Thousands of small molecule drugs or biological materials,especially antibody-based ICIs,are actively being studied and antibodies are currently widely used.Limitations,such as anti-tumor efficacy,poor membrane permeability,and unneglected tolerance issues of antibody-based ICIs,remain evident but are thought to be overcome by small molecule drugs.Recent structural studies have broadened the scope of candidate immune checkpoint molecules,as well as innovative chemical inhibitors.By way of comparison,small molecule drug-based ICIs represent superior oral bioavailability and favorable pharmacokinetic features.Several ongoing clinical trials are exploring the synergetic effect of ICIs and other therapeutic strategies based on multiple ICI functions,including immune regulation,anti-angiogenesis,and cell cycle regulation.In this review we summarized the current progression of small molecule ICIs and the mechanism underlying immune checkpoint proteins,which will lay the foundation for further exploration.

A stable implicit nodal integration-based particle finite element method(N-PFEM)for modelling saturated soil dynamics

In this study,we present a novel nodal integration-based particle finite element method(N-PFEM)designed for the dynamic analysis of saturated soils.Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner(HR)variational principle,creating an implicit PFEM formulation.To mitigate the volumetric locking issue in low-order elements,we employ a node-based strain smoothing technique.By discretising field variables at the centre of smoothing cells,we achieve nodal integration over cells,eliminating the need for sophisticated mapping operations after re-meshing in the PFEM.We express the discretised governing equations as a min-max optimisation problem,which is further reformulated as a standard second-order cone programming(SOCP)problem.Stresses,pore water pressure,and displacements are simultaneously determined using the advanced primal-dual interior point method.Consequently,our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation.Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy,obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches.This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.

Adaptive Optimal Discrete-Time Output-Feedback Using an Internal Model Principle and Adaptive Dynamic Programming

In order to address the output feedback issue for linear discrete-time systems, this work suggests a brand-new adaptive dynamic programming(ADP) technique based on the internal model principle(IMP). The proposed method, termed as IMP-ADP, does not require complete state feedback-merely the measurement of input and output data. More specifically, based on the IMP, the output control problem can first be converted into a stabilization problem. We then design an observer to reproduce the full state of the system by measuring the inputs and outputs. Moreover, this technique includes both a policy iteration algorithm and a value iteration algorithm to determine the optimal feedback gain without using a dynamic system model. It is important that with this concept one does not need to solve the regulator equation. Finally, this control method was tested on an inverter system of grid-connected LCLs to demonstrate that the proposed method provides the desired performance in terms of both tracking and disturbance rejection.

Cytokine release syndrome triggered by programmed death 1 blockade(sintilimab)therapy in a psoriasis patient:A case report

BACKGROUND In recent years,immune checkpoint inhibitors(ICIs)have demonstrated remarkable efficacy across diverse malignancies.Notably,in patients with advanced gastric cancer,the use of programmed death 1(PD-1)blockade has significantly prolonged overall survival,marking a pivotal advancement comparable to the impact of Herceptin over the past two decades.While the therapeutic benefits of ICIs are evident,the increasing use of immunotherapy has led to an increase in immune-related adverse events.CASE SUMMARY This article presents the case of a patient with advanced gastric cancer and chronic plaque psoriasis.Following sintilimab therapy,the patient developed severe rashes accompanied by cytokine release syndrome(CRS).Fortunately,effective management was achieved through the administration of glucocorticoid,tocilizumab,and acitretin,which resulted in favorable outcomes.CONCLUSION Glucocorticoid and tocilizumab therapy was effective in managing CRS after PD-1 blockade therapy for gastric cancer in a patient with chronic plaque psoriasis.

Immunotherapy for esophageal cancer:Where are we now and where can we go

Immune checkpoint inhibitor therapy has dramatically improved patient prognosis,and thereby transformed the treatment in various cancer types including esophageal squamous cell carcinoma(ESCC)in the past decade.Monoclonal antibodies that selectively inhibit programmed cell death-1(PD-1)activity has now become standard of care in the treatment of ESCC in metastatic settings,and has a high expectation to provide clinical benefit during perioperative period.Further,anti-cytotoxic T-lymphocyte–associated protein 4(CTLA-4)monoclonal antibody has also been approved in the treatment of recurrent/metastatic ESCC in combination with anti-PD-1 antibody.Well understanding of the existing evidence of immune-based treatments for ESCC,as well as recent clinical trials on various combinations with chemotherapy for different clinical settings including neoadjuvant,adjuvant,and metastatic diseases,may provide future prospects of ESCC treatment for better patient outcomes.

Immune signature of small bowel adenocarcinoma and the role of tumor microenvironment

In this editorial we comment on the article published“Clinical significance of programmed cell death-ligand expression in small bowel adenocarcinoma is determined by the tumor microenvironment”.Small bowel adenocarcinoma(SBA)is a rare gastrointestinal neoplasm and despite the small intestine's significant surface area,SBA accounts for less than 3%of such tumors.Early detection is challenging and the reason arises from its asymptomatic nature,often leading to late-stage discovery and poor prognosis.Treatment involves platinum-based chemotherapy with a 5-fluorouracil combination,but the lack of effective chemotherapy contributes to a generally poor prognosis.SBAs are linked to genetic disorders and risk factors,including chronic inflammatory conditions.The unique characteristics of the small bowel,such as rapid cell renewal and an active immune system,contributes to the rarity of these tumors as well as the high intratumoral infiltration of immune cells is associated with a favorable prognosis.Programmed cell death-ligand 1(PD-L1)expression varies across different cancers,with potential discrepancies in its prognostic value.Microsatellite instability(MSI)in SBA is associated with a high tumor mutational burden,affecting the prognosis and response to immunotherapy.The presence of PD-L1 and programmed cell death 1,along with tumor-infiltrating lymphocytes,plays a crucial role in the complex microenvironment of SBA and contributes to a more favorable prognosis,especially in the context of high MSI tumors.Stromal tumor-infiltrating lymphocytes are identified as independent prognostic indicators and the association between MSI status and a favorable prognosis,emphasizes the importance of evaluating the immune status of tumors for treatment decisions.

Exploring Artistic Embeddings in Service Design:A Keyword-Driven Approach for Artwork Search and Recommendations

As living standards improve,the demand for artworks has been escalating,transcending beyond the realm of mere basic human necessities.However,amidst an extensive array of artwork choices,users often struggle to swiftly and accurately identify their preferred piece.In such scenarios,a recommendation system can be invaluable,assisting users in promptly pinpointing the desired artworks for better service design.Despite the escalating demand for artwork recommendation systems,current research fails to adequately meet these needs.Predominantly,existing artwork recommendation methodologies tend to disregard users’implicit interests,thereby overestimating their capability to articulate their preferences in full and often neglecting the nuances of their diverse interests.In response to these challenges,we have developed a weighted artwork correlation graph and put forth an embedding-based keyword-driven artwork search and recommendation methodology.Our approach transforms the keywords that delineate user interests into word embedding vectors.This allows for an effective distinction between the user’s core and peripheral interests.Subsequently,we employ a dynamic programming algorithm to extract artworks from the correlation graph,thereby obtaining artworks that align with the user’s explicit keywords and implicit interests.We have conducted an array of experiments using real-world datasets to validate our approach.The results attest to the superiority of our method in terms of its efficacy in searching and recommending artworks.

Quercetin Alleviates Lipopolysaccharide-Induced Cardiac Inflammation via Inhibiting Autophagy and Programmed Cell Death

Objective The aim of this study is to explore the potential modulatory role of quercetin against Endotoxin or lipopolysaccharide(LPS)induced septic cardiac dysfunction.Methods Specific pathogen-free chicken embryos(n=120)were allocated untreated control,phosphate buffer solution(PBS)vehicle,PBS with ethanol vehicle,LPS(500 ng/egg),LPS with quercetin treatment(10,20,or 40 nmol/egg,respectively),Quercetin groups(10,20,or 40 nmol/egg).Fifteenday-old embryonated eggs were inoculated with abovementioned solutions via the allantoic cavity.At embryonic day 19,the hearts of the embryos were collected for histopathological examination,RNA extraction,real-time polymerase chain reaction,immunohistochemical investigations,and Western blotting.Results They demonstrated that the heart presented inflammatory responses after LPS induction.The LPS-induced higher mRNA expressions of inflammation-related factors(TLR4,TNFα,MYD88,NF-κB1,IFNγ,IL-1β,IL-8,IL-6,IL-10,p38,MMP3,and MMP9)were blocked by quercetin with three dosages.Quercetin significantly decreased immunopositivity to TLR4 and MMP9 in the treatment group when compared with the LPS group.Quercetin significantly decreased protein expressions of TLR4,IFNγ,MMP3,and MMP9 when compared with the LPS group.Quercetin treatment prevented LPS-induced increase in the mRNA expression of Claudin 1 and ZO-1,and significantly decreased protein expression of claudin 1 when compared with the LPS group.Quercetin significantly downregulated autophagyrelated gene expressions(PPARα,SGLT1,APOA4,AMPKα1,AMPKα2,ATG5,ATG7,Beclin-1,and LC3B)and programmed cell death(Fas,Bcl-2,CASP1,CASP12,CASP3,and RIPK1)after LPS induction.Quercetin significantly decreased immunopositivity to APOA4,AMPKα2,and LC3-II/LC3-I in the treatment group when compared with the LPS group.Quercetin significantly decreased protein expressions of AMPKα1,LC3-I,and LC3-II.Quercetin significantly decreased the protein expression to CASP1 and CASP3 by immunohistochemical investigation or Western blotting in treatment group when compared with LPS group.Conclusion Quercetin alleviates cardiac inflammation induced by LPS through modulating autophagy,programmed cell death,and myocardiocytes permeability.

In vivo astrocyte reprogramming following spinal cord injury

Harmful and helpful roles of astrocytes in spinal cord injury(SCI):SCI induce gradable sensory,motor and autonomic impairments that correlate with the lesion severity and the rostro-caudal location of the injury site.The absence of spontaneous axonal regeneration after injury results from neuron-intrinsic and neuron-extrinsic parameters.Indeed,not only adult neurons display limited capability to regrow axons but also the injury environment contains inhibitors to axonal regeneration and a lack of growth-promoting factors.Amongst other cell populations that respond to the lesion,reactive astrocytes were first considered as only detrimental to spontaneous axonal regeneration.Indeed,astrocytes.

Metabolic reprogramming in skeletal cell differentiation

The human skeleton is a multifunctional organ made up of multiple cell types working in concert to maintain bone and mineral homeostasis and to perform critical mechanical and endocrine functions.From the beginning steps of chondrogenesis that prefigures most of the skeleton,to the rapid bone accrual during skeletal growth,followed by bone remodeling of the mature skeleton,cell differentiation is integral to skeletal health.

Multi-Timescale Distributed Approach to Generalized-Nash-Equilibrium Seeking in Noncooperative Nonconvex Games

Dear Editor,The distributed generalized-Nash-equilibrium(GNE)seeking in noncooperative games with nonconvexity is the topic of this letter.Inspired by the sequential quadratic programming(SQP)method,a multi-timescale multi-agent system(MAS)is developed,and its convergence to a critical point of the game is proven.To illustrate the qualities and efficacy of the theoretical findings,a numerical example is elaborated.