• Occlusion: is there a third way? A discussion paper.

      Davies, Stephen; email: stephen.j.davies@manchester.ac.uk; Dawson, Philip; Weerapperuma, Indika; Waring, David; Beddis, Hannah; Leven, Johanna; Aminian, Amin; Rayarel, Ashish; Cowan, Callum; Crawford, Charles; et al. (2021-08-13)
      This paper does not set out to describe the reasons why a new concept of dental care should be deemed as acceptable and recognised as mainstream. Rather, the starting point of this paper is the belief that some dentists who are increasing the overall vertical dimension for worn dentition patients are not using the protocols of the traditional 're-organised approach'. If adhesive direct restorations are used, there seems to be anecdotal indication that despite not restoring in the terminal hinge axis, it can have a successful outcome.So, while not criticising this approach simply because it does not follow orthodoxy, the paper has two objectives. It hopes to stimulate some debate and research on this subject. Furthermore, by suggesting some parameters for what might be considered a new approach, it aims to improve patient outcome. [Abstract copyright: © 2021. The Author(s), under exclusive licence to the British Dental Association.]
    • Off the couch: a psychiatrist’s candid stories of hope and healing

      Loewenthal, Kate Miriam; orcid: 0000-0001-7667-7809 (Informa UK Limited, 2021-07-09)
    • Off the couch: a psychiatrist’s candid stories of hope and healing

      Loewenthal, Kate Miriam; orcid: 0000-0001-7667-7809 (Informa UK Limited, 2021-07-09)
    • Offline crime bounces back to pre-COVID levels, cyber stays high: interrupted time-series analysis in Northern Ireland

      Buil-Gil, David; orcid: 0000-0002-7549-6317; email: david.builgil@manchester.ac.uk; Zeng, Yongyu; Kemp, Steven (Springer Berlin Heidelberg, 2021-11-10)
      Abstract: Much research has shown that the first lockdowns imposed in response to the COVID-19 pandemic were associated with changes in routine activities and, therefore, changes in crime. While several types of violent and property crime decreased immediately after the first lockdown, online crime rates increased. Nevertheless, little research has explored the relationship between multiple lockdowns and crime in the mid-term. Furthermore, few studies have analysed potentially contrasting trends in offline and online crimes using the same dataset. To fill these gaps in research, the present article employs interrupted time-series analysis to examine the effects on offline and online crime of the three lockdown orders implemented in Northern Ireland. We analyse crime data recorded by the police between April 2015 and May 2021. Results show that many types of traditional offline crime decreased after the lockdowns but that they subsequently bounced back to pre-pandemic levels. In contrast, results appear to indicate that cyber-enabled fraud and cyber-dependent crime rose alongside lockdown-induced changes in online habits and remained higher than before COVID-19. It is likely that the pandemic accelerated the long-term upward trend in online crime. We also find that lockdowns with stay-at-home orders had a clearer impact on crime than those without. Our results contribute to understanding how responses to pandemics can influence crime trends in the mid-term as well as helping identify the potential long-term effects of the pandemic on crime, which can strengthen the evidence base for policy and practice.
    • Older adults’ construal of sedentary behaviour: Implications for reducing sedentary behaviour in older adult populations

      McGowan, Laura J; orcid: 0000-0002-4054-9300; email: laura.mcgowan@manchester.ac.uk; Powell, Rachael; French, David P; orcid: 0000-0002-7663-7804 (SAGE Publications, 2020-03-01)
      Older adults are the most sedentary age group, with sedentary behaviour having negative health-related consequences. There is currently limited understanding of how older adults view sedentary behaviour. This study investigated older adults’ understanding of the concept of sedentary behaviour. Semi-structured interviews were conducted with 22 community-dwelling older adults in urban North-West England, selected to be diverse in socio-economic background and activity levels. Interviews were recorded and transcribed verbatim. An inductive thematic analysis was conducted. Participants often construed sedentary behaviour as synonymous with a lack of physical activity, and many perceived reducing sedentary behaviour and increasing moderate-to-vigorous physical activity to be the same thing. Participants perceived the term ‘sedentary’ to have negative connotations and were often judgemental of people who engaged in high levels of sedentary behaviour. Most participants considered reducing sedentary behaviour to be of value, though more active individuals were unconvinced that reducing sedentary behaviour has value beyond the benefits of being physically active. Interventions may wish to provide education to address the misconception that increasing moderate-to-vigorous physical activity is necessary in order to reduce sedentary behaviour. Educating older adults on the independent health consequences of sedentary behaviour may also prove beneficial.
    • On prediction of aided behavioural measures using speech auditory brainstem responses and decision trees

      editor: Menezes, Pedro de Lemos; Perugia, Emanuele; orcid: 0000-0002-4392-6933; email: emanuele.perugia@manchester.ac.uk; BinKhamis, Ghada; orcid: 0000-0002-7696-1073; Schlittenlacher, Josef; Kluk, Karolina; orcid: 0000-0003-3638-2787; email: karolina.kluk@manchester.ac.uk (Public Library of Science, 2021-11-16)
      Current clinical strategies to assess benefits from hearing aids (HAs) are based on self-reported questionnaires and speech-in-noise (SIN) tests; which require behavioural cooperation. Instead, objective measures based on Auditory Brainstem Responses (ABRs) to speech stimuli would not require the individuals’ cooperation. Here, we re-analysed an existing dataset to predict behavioural measures with speech-ABRs using regression trees. Ninety-two HA users completed a self-reported questionnaire (SSQ-Speech) and performed two aided SIN tests: sentences in noise (BKB-SIN) and vowel-consonant-vowels (VCV) in noise. Speech-ABRs were evoked by a 40 ms [da] and recorded in 2x2 conditions: aided vs. unaided and quiet vs. background noise. For each recording condition, two sets of features were extracted: 1) amplitudes and latencies of speech-ABR peaks, 2) amplitudes and latencies of speech-ABR F0 encoding. Two regression trees were fitted for each of the three behavioural measures with either feature set and age, digit-span forward and backward, and pure tone average (PTA) as possible predictors. The PTA was the only predictor in the SSQ-Speech trees. In the BKB-SIN trees, performance was predicted by the aided latency of peak F in quiet for participants with PTAs between 43 and 61 dB HL. In the VCV trees, performance was predicted by the aided F0 encoding latency and the aided amplitude of peak VA in quiet for participants with PTAs ≤ 47 dB HL. These findings indicate that PTA was more informative than any speech-ABR measure, as these were relevant only for a subset of the participants. Therefore, speech-ABRs evoked by a 40 ms [da] are not a clinical predictor of behavioural measures in HA users.
    • On the Derivation of Multisymplectic Variational Integrators for Hyperbolic PDEs Using Exponential Functions

      Kosmas, Odysseas; orcid: 0000-0002-7047-9438; email: odysseas.kosmas@manchester.ac.uk; Boom, Pieter; orcid: 0000-0001-7437-277X; email: pieter.boom@manchester.ac.uk; Jivkov, Andrey P.; orcid: 0000-0002-3454-7341; email: andrey.jivkov@manchester.ac.uk (MDPI, 2021-08-25)
      We investigated the derivation of numerical methods for solving partial differential equations, focusing on those that preserve physical properties of Hamiltonian systems. The formulation of these properties via symplectic forms gives rise to multisymplectic variational schemes. By using analogy with the smooth case, we defined a discrete Lagrangian density through the use of exponential functions, and derived its Hamiltonian by Legendre transform. This led to a discrete Hamiltonian system, the symplectic forms of which obey the conservation laws. The integration schemes derived in this work were tested on hyperbolic-type PDEs, such as the linear wave equations and the non-linear seismic wave equations, and were assessed for their accuracy and the effectiveness by comparing them with those of standard multisymplectic ones. Our error analysis and the convergence plots show significant improvements over the standard schemes.
    • On the Geometric Description of Nonlinear Elasticity via an Energy Approach Using Barycentric Coordinates

      Kosmas, Odysseas; orcid: 0000-0002-7047-9438; email: odysseas.kosmas@manchester.ac.uk; Boom, Pieter; email: pieter.boom@manchester.ac.uk; Jivkov, Andrey P.; orcid: 0000-0002-3454-7341; email: andrey.jivkov@manchester.ac.uk (MDPI, 2021-07-19)
      The deformation of a solid due to changing boundary conditions is described by a deformation gradient in Euclidean space. If the deformation process is reversible (conservative), the work done by the changing boundary conditions is stored as potential (elastic) energy, a function of the deformation gradient invariants. Based on this, in the present work we built a “discrete energy model” that uses maps between nodal positions of a discrete mesh linked with the invariants of the deformation gradient via standard barycentric coordinates. A special derivation is provided for domains tessellated by tetrahedrons, where the energy functionals are constrained by prescribed boundary conditions via Lagrange multipliers. The analysis of these domains is performed via energy minimisation, where the constraints are eliminated via pre-multiplication of the discrete equations by a discrete null-space matrix of the constraint gradients. Numerical examples are provided to verify the accuracy of the proposed technique. The standard barycentric coordinate system in this work is restricted to three-dimensional (3-D) convex polytopes. We show that for an explicit energy expression, applicable also to non-convex polytopes, the general barycentric coordinates constitute fundamental tools. We define, in addition, the discrete energy via a gradient for general polytopes, which is a natural extension of the definition for discrete domains tessellated by tetrahedra. We, finally, prove that the resulting expressions can consistently describe the deformation of solids.
    • On Thresholds for Dynamic Strength in Solids

      Bourne, N. K.; orcid: 0000-0002-8883-1196; email: neil.bourne@manchester.ac.uk (Springer International Publishing, 2021-04-20)
      Abstract: The limits of elastic behaviour change with the nature of the impulse applied to a target and the size of volume interrogated by a measurement, since it is the pre-existing defects sampled within its rise that determine the response observed. This review considers a range of solids of different material classes and tracks the development of the strength of the material during shock loading, from yield at the Hugoniot elastic limit, across the weak shock regime, to its transition to strong shock behaviour. It is shown that at this stress, the weak shock limit (WSL), the shear component of the applied stress exceeds the theoretical strength of the material. Beyond this threshold, there are a number of new responses that confirm a transition from an inhomogeneous to a homogeneous state. Further, whilst strength rises across the weak shock regime, it saturates at the WSL. For instance, failure in shocked glasses transitions from localised fracture initiated at target boundaries to a global failure at this threshold at the theoretical strength. Sapphire′s strength asymptotes to the theoretical strength of the strongest direction in its lattice. Finally, the fourth-power dependence of strain rate upon stress appears to be a consequence of the homogeneous flow in the strong shock regime. This review suggests that µ/2π is a good approximation for the unrelaxed theoretical strength of solids at increasing stresses beyond the WSL. The methodology unfolded here represents a new means to experimentally determine the ultimate shear strength of solids.
    • On Thresholds for Dynamic Strength in Solids

      Bourne, N. K.; orcid: 0000-0002-8883-1196; email: neil.bourne@manchester.ac.uk (Springer International Publishing, 2021-04-20)
      Abstract: The limits of elastic behaviour change with the nature of the impulse applied to a target and the size of volume interrogated by a measurement, since it is the pre-existing defects sampled within its rise that determine the response observed. This review considers a range of solids of different material classes and tracks the development of the strength of the material during shock loading, from yield at the Hugoniot elastic limit, across the weak shock regime, to its transition to strong shock behaviour. It is shown that at this stress, the weak shock limit (WSL), the shear component of the applied stress exceeds the theoretical strength of the material. Beyond this threshold, there are a number of new responses that confirm a transition from an inhomogeneous to a homogeneous state. Further, whilst strength rises across the weak shock regime, it saturates at the WSL. For instance, failure in shocked glasses transitions from localised fracture initiated at target boundaries to a global failure at this threshold at the theoretical strength. Sapphire′s strength asymptotes to the theoretical strength of the strongest direction in its lattice. Finally, the fourth-power dependence of strain rate upon stress appears to be a consequence of the homogeneous flow in the strong shock regime. This review suggests that µ/2π is a good approximation for the unrelaxed theoretical strength of solids at increasing stresses beyond the WSL. The methodology unfolded here represents a new means to experimentally determine the ultimate shear strength of solids.
    • Online screencasting tutorials: A way forward for legal resources training?

      Peters, Lisa; University of Chester (Cambridge University Press, 2011)
      This journal articles discusses the using screencasting (video tutorials) in legal resources training.
    • Open questions in organic crystal polymorphism

      Cruz-Cabeza, Aurora J.; orcid: 0000-0002-0957-4823; email: aurora.cruzcabeza@manchester.ac.uk; Feeder, Neil; Davey, Roger J. (Nature Publishing Group UK, 2020-10-19)
      Polymorphs, crystals with different structure and properties but the same molecular composition, arise from the subtle interplay between thermodynamics and kinetics during crystallisation. In this opinion piece, the authors review the latest developments in the field of polymorphism and discuss standing open questions.
    • Opinion of the Scientific Committee on Consumer safety (SCCS) – Final Opinion on propylparaben (CAS No 94-13-3, EC No 202-307-7)

      Bodin, Laurent; Rogiers, Vera; Bernauer, Ulrike; Chaudhry, Qasim; Coenraads, Pieter Jan; orcid: 0000-0001-9458-7129; Dusinska, Maria; Ezendam, Janine; Gaffet, Eric; Galli, Corrado Ludovico; Granum, Berit; et al.
      In cosmetic products, the ingredient propylparaben (CAS No 94-13-3, EC No 202-307-7) with the chemical names Propyl 4-hydroxybenzoate and 4-Hydroxybenzoic acid propyl ester is currently regulated as a preservative in a concentration up to 0.14 % (as acid) (Annex V/12a). In addition, a safe concentration was established for mixtures of parabens, where the sum of the individual concentrations should not exceed 0.8 % (as acid). However, in such mixtures the sum of the individual concentrations of butyl- and propylparaben and their salts should not exceed 0.14 %. Propylparaben was subject to different safety evaluations in 2005 (SCCP/0874/05), 2006 (SCCP/1017/06), 2008 (SCCP/1183/08), 2010 (SCCS/1348/10), 2011 (SCCS/1446/11), 2013 (SCCS/1514/13). On the basis of the safety assessment of propylparaben, and considering the concerns related to potential endocrine disrupting properties, the SCCS has concluded that propylparaben is safe when used as a preservative in cosmetic products up to a maximum concentration of 0.14 %. The available data on propylparaben provide some indications for potential endocrine effects. However, the current level of evidence is not sufficient to regard it as an endocrine disrupting substance, or to derive a toxicological point of departure based on endocrine disrupting properties for use in human health risk assessment. The SCCS mandates do not address environmental aspects. Therefore, this assessment did not cover the safety of propylparaben for the environment.
    • Opportunity Costs Pacifism

      Pattison, James; orcid: 0000-0002-4649-358X; email: james.pattison@manchester.ac.uk (Springer Netherlands, 2020-05-26)
      Abstract: If the resources used to wage wars could be spent elsewhere and save more lives, does this mean that wars are unjustified? This article considers this question, which has been largely overlooked by Just War Theorists and pacifists. It focuses on whether the opportunity costs of war lead to a form of pacifism, which it calls ‘Opportunity Costs Pacifism’. The article argues that Opportunity Costs Pacifism is, at the more ideal level, compelling. It suggests that the only plausible response to Opportunity Costs Pacifism applies in highly nonideal circumstances. This has major implications for Just War Theory and pacifism since it is only at the highly nonideal level that war can be justified.
    • Optimal Utility of H-Reflex RDD as a Biomarker of Spinal Disinhibition in Painful and Painless Diabetic Neuropathy

      Worthington, Anne; orcid: 0000-0002-2331-3750; email: anne.worthington@postgrad.manchester.ac.uk; Kalteniece, Alise; email: alise.kalteniece@manchester.ac.uk; Ferdousi, Maryam; orcid: 0000-0002-7989-8233; email: maryam.ferdousi@manchester.ac.uk; D’Onofrio, Luca; orcid: 0000-0003-3905-0139; email: luca.donofrio@uniroma1.it; Dhage, Shaishav; email: Shaishav.Dhage@christie.nhs.uk; Azmi, Shazli; email: shazli.azmi@manchester.ac.uk; Adamson, Clare; email: clare.adamson@mft.nhs.uk; Hamdy, Shaheen; email: Shaheen.Hamdy@manchester.ac.uk; Malik, Rayaz A.; orcid: 0000-0002-7188-8903; email: ram2045@qatar-med.cornell.edu; Calcutt, Nigel A.; email: ncalcutt@health.ucsd.edu; et al. (MDPI, 2021-07-12)
      Impaired rate-dependent depression of the Hoffman reflex (HRDD) is a potential biomarker of impaired spinal inhibition in patients with painful diabetic neuropathy. However, the optimum stimulus-response parameters that identify patients with spinal disinhibition are currently unknown. We systematically compared HRDD, performed using trains of 10 stimuli at five stimulation frequencies (0.3, 0.5, 1, 2 and 3 Hz), in 42 subjects with painful and 62 subjects with painless diabetic neuropathy with comparable neuropathy severity, and 34 healthy controls. HRDD was calculated using individual and mean responses compared to the initial response. At stimulation frequencies of 1, 2 and 3 Hz, HRDD was significantly impaired in patients with painful diabetic neuropathy compared to patients with painless diabetic neuropathy for all parameters and for most parameters when compared to healthy controls. HRDD was significantly enhanced in patients with painless diabetic neuropathy compared to controls for responses towards the end of the 1 Hz stimulation train. Receiver operating characteristic curve analysis in patients with and without pain showed that the area under the curve was greatest for response averages of stimuli 2–4 and 2–5 at 1 Hz, AUC = 0.84 (95%CI 0.76–0.92). Trains of 5 stimuli delivered at 1 Hz can segregate patients with painful diabetic neuropathy and spinal disinhibition, whereas longer stimulus trains are required to segregate patients with painless diabetic neuropathy and enhanced spinal inhibition.
    • Optimising Large Animal Models of Sustained Atrial Fibrillation: Relevance of the Critical Mass Hypothesis

      Denham, Nathan C.; email: Nathan.denham@manchester.ac.uk; Pearman, Charles M.; Madders, George W. P.; Smith, Charlotte E. R.; Trafford, Andrew W.; Dibb, Katharine M. (Frontiers Media S.A., 2021-06-15)
      Background: Large animal models play an important role in our understanding of the pathophysiology of atrial fibrillation (AF). Our aim was to determine whether prospectively collected baseline variables could predict the development of sustained AF in sheep, thereby reducing the number of animals required in future studies. Our hypothesis was that the relationship between atrial dimensions, refractory periods and conduction velocity (otherwise known as the critical mass hypothesis) could be used for the first time to predict the development of sustained AF. Methods: Healthy adult Welsh mountain sheep underwent a baseline electrophysiology study followed by implantation of a neurostimulator connected via an endocardial pacing lead to the right atrial appendage. The device was programmed to deliver intermittent 50 Hz bursts of 30 s duration over an 8-week period whilst sheep were monitored for AF. Results: Eighteen sheep completed the protocol, of which 28% developed sustained AF. Logistic regression analysis showed only fibrillation number (calculated using the critical mass hypothesis as the left atrial diameter divided by the product of atrial conduction velocity and effective refractory period) was associated with an increased likelihood of developing sustained AF (Ln Odds Ratio 26.1 [95% confidence intervals 0.2–52.0] p = 0.048). A receiver-operator characteristic curve showed this could be used to predict which sheep developed sustained AF (C-statistic 0.82 [95% confidence intervals 0.59–1.04] p = 0.04). Conclusion: The critical mass hypothesis can be used to predict sustained AF in a tachypaced ovine model. These findings can be used to optimise the design of future studies involving large animals.
    • Optimising use of 4D-CT phase information for radiomics analysis in lung cancer patients treated with stereotactic body radiotherapy

      Davey, Angela; orcid: 0000-0002-8377-5113; email: angela.davey@postgrad.manchester.ac.uk; van Herk, Marcel; Faivre-Finn, Corinne; Brown, Sean; McWilliam, Alan (IOP Publishing, 2021-05-24)
      Abstract: Purpose. 4D-CT is routine imaging for lung cancer patients treated with stereotactic body radiotherapy. No studies have investigated optimal 4D phase selection for radiomics. We aim to determine how phase data should be used to identify prognostic biomarkers for distant failure, and test whether stability assessment is required. A phase selection approach will be developed to aid studies with different 4D protocols and account for patient differences. Methods. 186 features were extracted from the tumour and peritumour on all phases for 258 patients. Feature values were selected from phase features using four methods: (A) mean across phases, (B) median across phases, (C) 50% phase, and (D) the most stable phase (closest in value to two neighbours), coined personalised selection. Four levels of stability assessment were also analysed, with inclusion of: (1) all features, (2) stable features across all phases, (3) stable features across phase and neighbour phases, and (4) features averaged over neighbour phases. Clinical-radiomics models were built for twelve combinations of feature type and assessment method. Model performance was assessed by concordance index (c-index) and fraction of new information from radiomic features. Results. The most stable phase spanned the whole range but was most often near exhale. All radiomic signatures provided new information for distant failure prediction. The personalised model had the highest c-index (0.77), and 58% of new information was provided by radiomic features when no stability assessment was performed. Conclusion. The most stable phase varies per-patient and selecting this improves model performance compared to standard methods. We advise the single most stable phase should be determined by minimising feature differences to neighbour phases. Stability assessment over all phases decreases performance by excessively removing features. Instead, averaging of neighbour phases should be used when stability is of concern. The models suggest that higher peritumoural intensity predicts distant failure.
    • Optimising use of 4D-CT phase information for radiomics analysis in lung cancer patients treated with stereotactic body radiotherapy

      Davey, Angela; orcid: 0000-0002-8377-5113; email: angela.davey@postgrad.manchester.ac.uk; van Herk, Marcel; Faivre-Finn, Corinne; Brown, Sean; McWilliam, Alan (IOP Publishing, 2021-05-24)
      Abstract: Purpose. 4D-CT is routine imaging for lung cancer patients treated with stereotactic body radiotherapy. No studies have investigated optimal 4D phase selection for radiomics. We aim to determine how phase data should be used to identify prognostic biomarkers for distant failure, and test whether stability assessment is required. A phase selection approach will be developed to aid studies with different 4D protocols and account for patient differences. Methods. 186 features were extracted from the tumour and peritumour on all phases for 258 patients. Feature values were selected from phase features using four methods: (A) mean across phases, (B) median across phases, (C) 50% phase, and (D) the most stable phase (closest in value to two neighbours), coined personalised selection. Four levels of stability assessment were also analysed, with inclusion of: (1) all features, (2) stable features across all phases, (3) stable features across phase and neighbour phases, and (4) features averaged over neighbour phases. Clinical-radiomics models were built for twelve combinations of feature type and assessment method. Model performance was assessed by concordance index (c-index) and fraction of new information from radiomic features. Results. The most stable phase spanned the whole range but was most often near exhale. All radiomic signatures provided new information for distant failure prediction. The personalised model had the highest c-index (0.77), and 58% of new information was provided by radiomic features when no stability assessment was performed. Conclusion. The most stable phase varies per-patient and selecting this improves model performance compared to standard methods. We advise the single most stable phase should be determined by minimising feature differences to neighbour phases. Stability assessment over all phases decreases performance by excessively removing features. Instead, averaging of neighbour phases should be used when stability is of concern. The models suggest that higher peritumoural intensity predicts distant failure.
    • Optimization of a Patient-Specific External Fixation Device for Lower Limb Injuries

      Alqahtani, Mohammed S.; orcid: 0000-0002-9178-8168; email: mohammed.alqahtani@manchester.ac.uk; Al-Tamimi, Abdulsalam Abdulaziz; email: aaaltamimi@KSU.EDU.SA; Hassan, Mohamed H.; orcid: 0000-0002-0832-8559; email: Mohamed.hassan@manchester.ac.uk; Liu, Fengyuan; email: fengyuan.liu@bristol.ac.uk; Bartolo, Paulo; orcid: 0000-0003-3683-726X; email: paulojorge.dasilvabartolo@manchester.ac.uk (MDPI, 2021-08-10)
      The use of external fixation devices is considered a valuable approach for the treatment of bone fractures, providing proper alignment to fractured fragments and maintaining fracture stability during the healing process. The need for external fixation devices has increased due to an aging population and increased trauma incidents. The design and fabrication of external fixations are major challenges since the shape and size of the defect vary, as well as the geometry of the human limb. This requires fully personalized external fixators to improve its fit and functionality. This paper presents a methodology to design personalized lightweight external fixator devices for additive manufacturing. This methodology comprises data acquisition, Computer tomography (CT) imaging analysis and processing, Computer Aided Design (CAD) modelling and two methods (imposed predefined patterns and topology optimization) to reduce the weight of the device. Finite element analysis with full factorial design of experiments were used to determine the optimal combination of designs (topology optimization and predefined patterns), materials (polylactic acid, acrylonitrile butadiene styrene, and polyamide) and thickness (3, 4, 5 and 6 mm) to maximize the strength and stiffness of the fixator, while minimizing its weight. The optimal parameters were found to correspond to an external fixator device optimized by topology optimization, made in polylactic acid with 4 mm thickness.
    • Optimization of competitive supply chains with retailers' horizontal cooperation and consumers' green preference.

      Shang, Wenfang; Teng, Liangliang; Yang, Jian-Bo; email: jian-bo.yang@manchester.ac.uk (2021-07-16)
      With the wider recognition of the concept of environmental protection and sustainable development, more and more manufacturers have begun to implement green manufacturing strategies. However, green development is a gradual process, and the coexistence of ordinary and green products is common. This paper examines the competition between ordinary products and green ones based on supply chains, and discusses the impact of retailers' horizontal cooperation on pricing, greenness, market demand, profit, and other related decisions and results. Model solutions and numerical experiments have shown that consumers' green preference (CGP) has a positive impact on the results of green products and negative effects on those of ordinary ones; however, the impact of competition intensity (CI) is more complex, and the trend tends to change if it exceeds a certain critical value. In general, cooperation encourages retailers to raise prices and make manufacturers lower wholesale prices, but the retail and wholesale prices of green products are always higher than the corresponding prices of ordinary ones. Market demand can be reduced due to cooperation, but it is conducive to strengthening green products' greenness. However, if CI exceeds a certain threshold, the greenness will be weakened by cooperation. Both retailers can benefit from cooperation easily and they always reach a win-win situation, but manufacturers suffer badly as a result. Nevertheless, when CI is weak, cooperation will bring a greater profit improvement to the whole chain of ordinary products; in this case, if a retailer is willing to compensate for a manufacturer's profit loss and help it benefit from cooperation, the manufacturer will encourage the retailer to cooperate horizontally with the green retailer, but the green chain will be seriously damaged. When CI is strong, the greenness of green products is not obvious enough, and cooperation can bring some chances to achieve a win-win situation for two chains; if the green retailer can obtain a larger share from cooperation under this scenario, it can also enable its manufacturer to obtain compensation and change the profit increment from negative to positive. From an overall perspective, when CI is very weak or very strong, horizontal cooperation is conducive to improving the profit of the entire supply chain competition system, but when CI is relatively flat, independent operation for each chain is more advantageous; if the competition status is stable and unchanged, independent competition will be superior to horizontal cooperation. [Abstract copyright: © 2021. The Author(s).]