• Cholesterol Homeostasis: An In Silico Investigation into How Aging Disrupts Its Key Hepatic Regulatory Mechanisms

      Morgan, Amy; Mc Auley, Mark; University of Chester
      The dysregulation of intracellular cholesterol homeostasis is associated with several age-related diseases, most notably cardiovascular disease (CVD). Research in this area has benefitted from using computational modelling to study the inherent complexity associated with the regulation of this system. In addition to facilitating hypothesis exploration, the utility of modelling lies in its ability to represent an array of rate limiting enzymatic reactions, together with multiple feedback loops, which collectively define the dynamics of cholesterol homeostasis. However, to date no model has specifically investigated the effects aging has on this system. This work addresses this shortcoming by explicitly focusing on the impact of aging on hepatic intracellular cholesterol homeostasis. The model was used to investigate the experimental findings that reactive oxygen species induce the total activation of 3-hydroxy-3-methylglutaryl-coenzyme A (HMG-CoA) reductase (HMGCR). Moreover, the model explored the impact of an age-related decrease in hepatic acetyl-CoA acetyltransferase 2 (ACAT2). The model suggested that an increase in the activity of HMGCR does not have as significant an impact on cholesterol homeostasis as a decrease in hepatic ACAT2 activity. According to the model, a decrease in the activity of hepatic ACAT2 raises free cholesterol (FC) and decreases low-density lipoprotein cholesterol (LDL-C) levels. Increased acetyl CoA synthesis resulted in a reduction in the number of hepatic low-density lipoprotein receptors, and increased LDL-C, FC, and cholesterol esters. The rise in LDL-C was restricted by elevated hepatic FC accumulation. Taken together these findings have important implications for healthspan. This is because emerging clinical data suggest hepatic FC accumulation is relevant to the pathogenesis of non-alcoholic fatty liver disease (NAFLD), which is associated with an increased risk of CVD. These pathophysiological changes could, in part, help to explain the phenomenon of increased mortality associated with low levels of LDL-C which have been observed in certain studies involving the oldest old (≥ 85 years).
    • Vibration energy harvesting of multifunctional carbon fibre composite laminate structures

      Alsaadi, Ahmed; Shi, Yu; Pan, Lei; Tao, Jie; Jia, Yu; University of Chester; Nanjing University of Aeronautics and Astronautics
      A sustainable power supply for a wide range of applications, such as powering sensors for structural health monitoring and wireless sensoring nodes for data transmission and communication used in unmanned air vehicles, automobiles, renewable energy sectors, and smart city technologies, is targeted. This paper presents an experimental and numerical study that describes an innovative technique to harvest energy resulted from environmental vibrations. A piezoelectric energy harvester was integrated onto a carbon fibre reinforced polymer (CFRP) laminate structure using the co-curing method. The integrated composite with the energy harvester was lightweight, flexible and provided robust and reliable energy outcomes, which can be used to power different low-powered wireless sensing nodes. A normalised power density of 97  μW cm−3m−2s4 was obtained from resonance frequency of 46 Hz sinusoidal waves at amplitude of 0.2 g; while the representative environmental vibration waves in various applications (aerospace, automotive, machine and bridge infrastructure) were experimentally and numerically investigated to find out the energy that can be harvested by such a multifunctional composite structure. The results showed the energy harvested at different vibration input from various industrial sectors could be sufficient to power an autonomous structural health monitoring system and wireless communications by the designed composite structure.
    • Dynamics of shadow system of a singular Gierer-Meinhardt system on an evolving domain

      Kavallaris, Nikos I.; Bareira, Raquel; Madzvamuse, Anotida; University of Chester; Polytechnic Institute of Setubal; University of Lisbon; Sussex University
      The main purpose of the current paper is to contribute towards the comprehension of the dynamics of the shadow system of a singular Gierer-Meinhardt model on an isotropically evolving domain. In the case where the inhibitor's response to the activator's growth is rather weak, then the shadow system of the Gierer-Meinhardt model is reduced to a single though non-local equation whose dynamics is thoroughly investigated throughout the manuscript. The main focus is on the derivation of blow-up results for this non-local equation, which can be interpreted as instability patterns of the shadow system. In particular, a diffusion-driven instability (DDI), or Turing instability, in the neighbourhood of a constant stationary solution, which then is destabilised via diffusion-driven blow-up, is observed. The latter indicates the formation of some unstable patterns, whilst some stability results of global-in-time solutions towards non-constant steady states guarantee the occurrence of some stable patterns. Most of the theoretical results are verified numerically, whilst the numerical approach is also used to exhibit the dynamics of the shadow system when analytical methods fail.
    • An overview of thermal necrosis: present and future

      Mediouni, Mohamed; Kucklick, Theodore; Poncet, Sébastien; Madiouni, Riadh; Abouaomar, Amine; Madry, Henning; Cucchiarini, Magali; Chopko, Bohdan; Vaughan, Neil; Arora, Manit; et al. (Informa UK Limited, 2019-05-10)
    • A review of organic waste enrichment for inducing palatability of black soldier fly larvae: Wastes to valuable resources

      Raksasat, Ratchaprapa; Lim, Jun Wei; Kiatkittipong, Worapon; Kiatkittipong, Kunlanan; Ho, Yeek Chia; Lam, Man Kee; Font Palma, Carolina; Zaid, Hayyiratul Fatimah Mohd; Cheng, Chin Kui; Universiti Teknologi PETRONAS; Silpakorn University; King Mongkut's Institute of Technology Ladkrabang; University of Chester; Khalifa University
      The increase of annual organic wastes generated worldwide has become a major problem for many countries since the mismanagement could bring about negative effects on the environment besides, being costly for an innocuous disposal. Recently, insect larvae have been investigated to valorize organic wastes. This entomoremediation approach is rising from the ability of the insect larvae to convert organic wastes into its biomass via assimilation process as catapulted by the natural demand to complete its lifecycle. Among the insect species, black soldier fly or Hermetia illucens is widely researched since the larvae can grow in various environments while being saprophagous in nature. Even though black soldier fly larvae (BSFL) can ingest various decay materials, some organic wastes such as sewage sludge or lignocellulosic wastes such as waste coconut endosperm are destitute of decent nutrients that could retard the BSFL growth. Hence, blending with nutrient-rich low-cost substrates such as palm kernel expeller, soybean curd residue, etc. is employed to fortify the nutritional contents of larval feeding substrates prior to administering to the BSFL. Alternatively, microbial fermentation can be adopted to breakdown the lignocellulosic wastes, exuding essential nutrients for growing BSFL. Upon reaching maturity, the BSFL can be harvested to serve as the protein and lipid feedstock. The larval protein can be made into insect meal for farmed animals, whilst the lipid source could be extracted and transesterified into larval biodiesel to cushion the global energy demands. Henceforth, this review presents the influence of various organic wastes introduced to feed BSFL, targeting to reduce wastes and producing biochemicals from mature larvae through entomoremediation. Modification of recalcitrant organic wastes via fermentation processes is also unveiled to ameliorate the BSFL growth. Lastly, the sustainable applications of harvested BSFL biomass are as well covered together with the immediate shortcomings that entail further researches.
    • Terahertz Signatures of Hydrate Formation in Alkali Halide Solutions

      Ligang, Chen; Ren, Guanhua; Liu, Liyuan; Guo, Pan; Wan, Endong; Zhou, Lu; Zhu, Zhonglie; Zhang, Jianbing; Yang, Bin; Zhang, Wentao; et al.
      We systematically studied the ability of 20 alkali halides to form solid hydrates in the frozen state from their aqueous solutions by terahertz time-domain spectroscopy combined with density functional theory (DFT) calculations. We experimentally observed the rise of new terahertz absorption peaks in the spectral range of 0.3-3.5 THz in frozen alkali halide solutions. The DFT calculations prove that the rise of observed new peaks in solutions containing Li+, Na+ or F‾ ions indicates the formation of salt hydrates, while that in other alkali halide solutions is caused by the splitting phonon modes of the imperfectly crystallized salts in ice. As a simple empirical rule, the correlation between the terahertz signatures and the ability of 20 alkali halides to form a hydrate has been established.
    • Domain wall free polar structure enhanced photodegradation activity in nanoscale ferroelectric BaxSr1-xTiO3

      Wang, Yaqiong; Zhang, Man; Jianguo, Liu; Zhang, Haibin; Li, Feng; Tseng, Chiao-Wei; Yang, Bin; Smith, Graham C.; Zhai, Jiwei; Zhang, Zhen; et al.
      Ferroelectric materials exhibit anomalous behavior due to the presence of domains and domain walls which are related to the spontaneous polarization inherent in the crystal structure. Control of ferroelectric domains and domain walls has been used to enhance device performances in ultrasound, pyroelectric detectors and photovoltaic systems with renewed interest in nanostructuring for energy applications. It is also known that the ferroelectric including domain walls can double photocatalytic rate and increase carrier lifetime from μs to ms[1] However, there remains a lack of understanding on the different contributions of the domain and domain walls to photo-catalytic activities. Herein it is found, by comparing samples of nanostructured BaxSr1 xTiO3 with and without a polar domain, that the material with polar domains has a faster reaction rate (k=0.18 min-1) than the non polar one (k = 0.11 min-1). It is further revealed that the observed enhanced photoactivity of perovskite ferroelectric materials stems from the inherent polarization of the domain instead of domain walls. Here, the new understanding of the underlying physics of materials with a spontaneous dipole opens a door to enhance the performance of light induced energy harvesting systems.
    • Capsule membranes encapsulated with smart nanogels for facile detection of trace lead(II) ions in water

      Liu, Wen Ying; Ju, Xiao Jie; Faraj, Yousef; He, Fan; Peng, Han Yu; Liu, Yu Qiong; Liu, Zhuang; Wang, Wei; Xie, Rui; Chu, Liang Yin; et al.
      A novel method based on capsule membranes encapsulated with smart nanogels is successfully developed for facilely detecting trace lead(II) (Pb2+) ions, which are hazardous to both human health and the environment because of their toxicity. The capsule membrane system is composed of a semi-permeable calcium alginate membrane and encapsulated poly(N-isopropylacrylamide-co-acryloylamidobenzo-18-crown-6) (PNB) nanogels. The semi-permeable membrane allows Pb2+ ions and water to pass through quickly, but rejects the encapsulated nanogels and polymers totally. As soon as Pb2+ ions appear in the aqueous environment and enter into the capsule, they can be specifically recognized by encapsulated PNB nanogels via forming 18-crown-6/Pb2+ complexes that cause a Pb2+-induced phase transition of PNB nanogels from hydrophobic to hydrophilic state. As a result, the osmotic pressure inside the capsule membrane increases remarkably, and thus the elastic capsule membrane isothermally swells upon the presence of Pb2+ ions in the environmental aqueous solution. The Pb2+-induced swelling degree of the capsule membrane is dependent on the concentration of Pb2+ ions ([Pb2+]) in water. Thus, the [Pb2+] value in water is able to be easily detected by directly measuring the Pb2+-induced isothermal swelling ratio of the capsule membrane, which we demonstrate by using 15 prepared capsule membranes arranged in a line. The Pb2+-induced swelling ratios of the capsule membrane groups are easily observed with the naked eye, and the detection limit of the [Pb2+] in water is 10-9 mol L-1. Such a proposed method provides an easy and efficient strategy for facile detection of trace threat analytes in water.
    • Simultaneous determination of dopamine, uric acid and estriol in maternal urine samples based on the synergetic effect of reduced graphene oxide, silver nanowires and silver nanoparticles in their ternary 3D nanocomposite

      Zhao, Qian; Faraj, Yousef; Liu, Lu Yue; Wang, Wei; Xie, Rui; Liu, Zhuang; Ju, Xiao Jie; Wei, Jie; Chu, Liang Yin; University of Chester; Sichuan University
      A facile and efficient electrochemical biosensing platform based on screen printed carbon electrode (SPCE) modified with three-dimensional (3D) nanocomposite consists of reduced graphene oxide (RGO) with the insertion of silver nanowires (AgNWs) followed by the anchoring of silver nanoparticles (AgNPs) is constructed as RGO/AgNWs/AgNPs/SPCE for the simultaneous determination of dopamine (DA), uric acid (UA) and estriol (EST). The morphology characteristic and surface elemental composition of RGO/AgNWs/AgNPs nanocomposite are investigated by field-emission scanning electron microscope, transmission electron microscope and X-ray photoelectron spectroscope. Cyclic voltammetry, electrochemical impedance spectroscopy, linear sweep voltammetry and differential pulse voltammetry are utilized to explore the electrochemical performances of the constructed electrodes. Due to abundant active sites and excellent electrocatalytic activity of the nanocomposite, the RGO/AgNWs/AgNPs/SPCE sensor exhibits well-resolved oxidation peaks and enhanced oxidation peak currents in the ternary mixture of DA, UA and EST with respective linear response ranges of 0.6 to 50 μM, 1 to 100 μM and 1 to 90 μM and detection limits (S/N = 3) of 0.16 μM, 0.58 μM and 0.58 μM, respectively. Moreover, the constructed biosensor exhibits good selectivity, reproducibility and stability, and excellent performance in determining DA, UA and EST in synthetic urine samples with excellent recovery. The results reveal that the RGO/AgNWs/AgNPs nanocomposite is a promising candidate for advanced electrode material in electrochemical sensing field and possesses great application prospects in further sensing researches.
    • An Endoscope Interface for Immersive Virtual Reality

      John, Nigel W.; Day, Thomas W.; Wardle, Terrence; University of Chester
      This is a work in progress paper that describes a novel endoscope interface designed for use in an immersive virtual reality surgical simulator. We use an affordable off the shelf head mounted display to recreate the operating theatre environment. A hand held controller has been adapted so that it feels like the trainee is holding an endoscope controller with the same functionality. The simulator allows the endoscope shaft to be inserted into a virtual patient and pushed forward to a target position. The paper describes how we have built this surgical simulator with the intention of carrying out a full clinical study in the near future.
    • A Framework for Web-Based Immersive Analytics

      John, Nigel; Ritsos, Panagiotis; Butcher, Peter W. S. (University of Chester, 2020-08-17)
      The emergence of affordable Virtual Reality (VR) interfaces has reignited the interest of researchers and developers in exploring new, immersive ways to visualise data. In particular, the use of open-standards Web-based technologies for implementing VR experiences in a browser aims to enable their ubiquitous and platform-independent adoption. In addition, such technologies work in synergy with established visualization libraries, through the HTML Document Object Model (DOM). However, creating Immersive Analytics (IA) experiences remains a challenging process, as the systems that are currently available require knowledge of game engines, such as Unity, and are often intrinsically restricted by their development ecosystem. This thesis presents a novel approach to the design, creation and deployment of Immersive Analytics experiences through the use of open-standards Web technologies. It presents <VRIA>, a Web-based framework for creating Immersive Analytics experiences in VR that was developed during this PhD project. <VRIA> is built upon WebXR, A-Frame, React and D3.js, and offers a visualization creation workflow which enables users of different levels of expertise to rapidly develop Immersive Analytics experiences for the Web. The aforementioned reliance on open standards and the synergies with popular visualization libraries make <VRIA> ubiquitous and platform-independent in nature. Moreover, by using WebXR’s progressive enhancement, the experiences <VRIA> is able to create are accessible on a plethora of devices. This thesis presents an elaboration on the motivation for focusing on open-standards Web technologies, presents the <VRIA> visualization creation workflow and details the underlying mechanics of our framework. It reports on optimisation techniques, integrated into <VRIA>, that are necessary for implementing Immersive Analytics experiences with the necessary performance profile on the Web. It discusses scalability implications of the framework and presents a series of use case applications that demonstrate the various features of <VRIA>. Finally, it describes the lessons learned from the development of the framework, discusses current limitations, and outlines further extensions.
    • Treating wastewater by indigenous microalgae strain in pilot platform located inside a municipal wastewater treatment plant

      Han, Jichang; Laurenz, Thomsen; Pan, Kehou; Wang, Pu; Wawilow, Tatjana; Osundeko, Olumayowa; Wang, Song; Theilen, Ulf; Thomsen, Claudia; Jacob University Bremen, Germany
      Various resources from a municipal wastewater treatment plant (MWTP) are available for microalgae cultivation plants, suggesting that a combination of these technologies can be used to produce microalgae biomass and remove contaminants at a low cost. In this study, the growth performance and nutrient removal efficiency of an indigenous Scenedesmus sp. in various wastewater media with different exchange patterns were investigated firstly, then transferred to a pilot-scale photobioreactor (located inside a MWTP) for bioremediation use. The temperature and pH of the platform were maintained at 15–30°C and 7.6, respectively. The NH+4− N, NO−3− N, and PO3−4− P of the wastewater could be reduced to below 0.05, 0.40, and 0.175 mg L–1, respectively. Our results indicate that microalgae cultivation using the resources of a MWTP can achieve high algal biomass productivity and nutrient removal rate. Our study also suggests that efficient technology for controlling zooplankton needs to be developed.
    • Systems biology and Nutrition

      Mc Auley, Mark
      Systems biology has established itself as a paradigm which has been adopted in order to integrate a wealth of omics data which has been generated in the last few decades. Nutrition research has gradually embraced the systems biology approach, and this holistic way of investigating biological systems is beginning to pay dividends for our understanding of diet and its relationship with health. This chapter presents an overview of the key strands of systems biology; these include, genomics, transcriptomics, proteomics, metabolomics, bioinformatics and computational modelling. I discuss how these techniques are being used to gain new insights into nutrition research. Moreover, I reveal how computational modelling is being used to unravel how ageing effects cholesterol and folate metabolism. The chapter concludes by providing an insight into how systems biology will be applied to nutrition research in the future.
    • DOMestic Energy Systems and Technologies InCubator (DOMESTIC) and indoor air quality of the built environment

      Li, Jinghua; Khalid, Yousaf; Phillips, Gavin J.; University of Chester
      Oral presentation at RMetS Students and Early Career Scientists Conference 2020 on research project DOMESTIC (DOMestic Energy Systems and Technologies InCubator), which aims to build a facility for the demonstration of domestic technologies and design methodologies (i.e. air quality, energy efficiency).
    • New Self-Dual Codes of Length 68 from a 2 × 2 Block Matrix Construction and Group Rings

      Bortos, Maria; Gildea, Joe; Kaya, Abidin; Korban, Adrian; Tylyshchak, Alexander; Uzhgorod National University, University of Chester, Harmony School of Technology, University of Chester, Uzhgorod National University
      Many generator matrices for constructing extremal binary self-dual codes of different lengths have the form G = (In | A); where In is the n x n identity matrix and A is the n x n matrix fully determined by the first row. In this work, we define a generator matrix in which A is a block matrix, where the blocks come from group rings and also, A is not fully determined by the elements appearing in the first row. By applying our construction over F2 +uF2 and by employing the extension method for codes, we were able to construct new extremal binary self-dual codes of length 68. Additionally, by employing a generalised neighbour method to the codes obtained, we were able to con- struct many new binary self-dual [68,34,12]-codes with the rare parameters $\gamma = 7$; $8$ and $9$ in $W_{68,2}$: In particular, we find 92 new binary self-dual [68,34,12]-codes.
    • Space Phased Array Antenna Developments: A Perspective on Structural Design

      Wang, Congsi; Wang, Yan; Lian, Peiyuan; Xu, Qian; Shi, Yu; Jia, Yu; Du, Biao; Liu, Jing; Tang, Baofu; Xue, Song; et al.
    • A Taylor-Surrogate-Model-Based Method for the Electrical Performance of Array Antennas Under Interval Position Errors

      Wang, Congsi; Yuan, Shuai; Gao, Wei; Jiang, Chao; Zhu, Cheng; Li, Peng; Wang, Zhihai; Peng, Xuelin; Shi, Yu; Xidian University; University of New South Wales; Hunan University; Nanjing Research Institute of Electronics Technology; University of Chester
      In this letter, a Taylor-surrogate-model-based method (TSMBM) is proposed to predict the bounds of power pattern of array antennas with interval position errors of antenna elements. The advantage of TSMBM is that it provides the approximate analytical solution of the problem with high precision and free of “wrapping effect.” First, the integral form of the Taylor surrogate model (IFTSM) of the distorted power pattern of array antennas is deduced. Then, the extrema point vector of IFTSM can be readily calculated within a set composed of bounds, –1 and 1. Finally, the bounds of the distorted power pattern are determined by submit- ting the extrema point vector of IFTSM to the distorted power pattern. Representative examples are presented to demonstrate the accuracy and effectiveness of the method.
    • In situ fabrication of carbon fibre–reinforced polymer composites with embedded piezoelectrics for inspection and energy harvesting applications

      Yan, Xue; Courtney, Charles; Bowen, Chris; Gathercole, Nicholas; Wen, Tao; Jia, Yu; Shi, Yu; Aerospace Research Institute of Material and Processing Technology; University of Bath; University of Chester
      Current in situ damage detection of fibre-reinforced composites typically uses sensors which are attached to the structure. This may make periodic inspection difficult for complex part geometries or in locations which are difficult to reach. To overcome these limitations, we examine the use of piezoelectric materials in the form of macro-fibre composites that are embedded into carbon fibre–reinforced polymer composites. Such a multi-material system can provide an in situ ability for damage detection, sensing or energy harvesting. In this work, the piezoelectric devices are embedded between the carbon fibre prepreg, and heat treated at elevated temperatures, enabling complete integration of the piezoelectric element into the structure. The impact of processing temperature on the properties of the macro-fibre composites are assessed, in particular with respect to the Curie temperature of the embedded ferroelectric. The mechanical properties of the carbon fibre–reinforced polymer composites are evaluated to assess the impact of the piezoelectric on tensile strength. The performance of the embedded piezoelectric devices to transmit and receive ultrasonic signals is evaluated, along with the potential to harvest power from mechanical strain for self-powered systems. Such an approach provides a route to create multi-functional materials.
    • Effect of Temperature on Electromagnetic Performance of Active Phased Array Antenna

      Wang, Yan; Wang, Congsi; Lian, Peiyuan; Xue, Sone; Liu, Jing; Gao, Wei; Shi, Yu; Wang, Zhihai; Yu, Kunpeng; Peng, Xuelin; et al.
      Active phased array antennas (APAAs) can suffer from the effects of harsh thermal environments, which are caused by the large quantity of power generated by densely packed T/R modules and external thermal impacts. The situation may be worse in the case of limited room and severe thermal loads, due to heat radiation and a low temperature sink. The temperature field of the antenna can be changed. Since large numbers of temperature-sensitive electronic components exist in T/R modules, excitation current output can be significantly affected and the electromagnetic performance of APAAs can be seriously degraded. However, due to a lack of quantitative analysis, it is difficult to directly estimate the effect of temperature on the electromagnetic performance of APAAs. Therefore, this study investigated the electromagnetic performance of APAAs as affected by two key factors—the uniformly distributed temperature field and the temperature gradient field—based on different antenna shapes and sizes, to provide theoretical guidance for their thermal design.
    • Efficient Surrogate Model-Assisted Evolutionary Algorithm for Electromagnetic Design Automation with Applications

      Akinsolu, Mobayode, O. (University of ChesterWrexham Glyndŵr UniversityWrexham Glyndwr University, 2019-10)
      In this thesis, the surrogate model-aware evolutionary search (SMAS) framework is extended for efficient interactive optimisation of multiple criteria electromagnetic (EM) designs and/or devices through a novel method called two-stage interactive efficient EM micro-actuator design optimisation (TIEMO). The first robust analytical and behavioural study of the SMAS framework is also carried out in this thesis to serve as a guide for the meticulous selection of multiple differential evolution (DE) mutation strategies to make SMAS fit for use in parallel computing environments. Based on the study of SMAS and the self-adaptive use of the selected multiple DE mutation strategies and reinforcement learning techniques, a novel method, parallel surrogate model-assisted evolutionary algorithm for EM design (PSAED) is proposed. PSAED is tested extensively using mathematical benchmark problems and numerical EM design problems. For all cases, the efficiency improvement of PSAED compared to state-of-the-art evolutionary algorithms (EAs) is demonstrated by the several times up to about 20 times speed improvement observed and the high quality of design solutions. PSAED is then applied to real-world EM design problems as two purposebuilt methods for antenna design and optimisation and high-performance microelectro-mechanical systems (MEMS) design and optimisation in parallel computing environments, parallel surrogate model-assisted hybrid DE for antenna optimisation (PSADEA) and adaptive surrogate model-assisted differential evolution for MEMS optimisation (ASDEMO), respectively. For all the real-world antenna and MEMS design cases, PSAED methods obtain very satisfactory design solutions using an affordable optimisation time and comparisons are made with available alternative methods. Results from the comparisons show that PSAED methods obtain very satisfactory design solutions in all runs using an affordable optimisation time in each, whereas the alternative methods fail and/or seldom succeed to obtain feasible or satisfactory design solutions. PSAED methods also show better robustness and stability. In the future, PSAED methods will be embedded into commercial CAD/CEM tools and will be further extended for use in higher-order parallel clusters.