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The effect of heat thermotherapy on cardiovascular function and cardiometabolic health
Get PDFHeat thermotherapy (HT) is a promising strategy to improve cardiovascular (CV) function. HT modalities such as sauna bathing and hot water immersion (HWI) have been shown to induce positive acute CV responses and long-term CV adaptations, including artery structural remodelling, lower resting blood pressure (BP), and improved endothelial function; all associated with a lower risk of CV disease. Furthermore, HT could be used alongside high-intensity interval exercise (HIIEx) to augment positive CV adaptations associated with HIIEx alone. Unfortunately, substantial heterogeneity within the HT literature prevents evidence-based HT prescription for CV health. Additionally, common HT strategies can be prolonged and uncomfortable for participants. Therefore, this thesis investigated the efficacy of HT to improve CV function (meta-analysis, Chapter 2) and assessed different HT protocols and their acute cardiovascular response in young, healthy adults (Chapters 4 and 5).
The meta-analysis (Chapter 2) revealed HT improves CV function, as shown by the positive CV response after a single bout of HT (reduced diastolic blood pressure (DBP), mean arterial pressure (MAP) and increased flow-mediated dilation)) and the longer-term CV adaptations (reduced resting DBP and MAP) following multiple bouts of HT. Health status nor age did not affect these changes, demonstrating that HT can improve CV function in various population demographics. Chapter 4 investigated whether a short, hot, neck-level, 30-minute bathing session (HWI30) can elicit a similar acute CV response as the 60-minute, shoulder/waist level immersion bathing session (HWI60). Additionally, it was hypothesised that there would be no meaningful CV response (i.e. lower BP) in the thermoneutral water immersion condition (TWI). There was a condition-by-time interaction effect for DBP, MAP, HR and core body temperature (Tc). Despite the higher Tc achieved during and post-bathing for HWI60 than HWI30, the heart rate (HR) elevation and reduction in DBP and MAP were similar for HWI30 and HWI60. Meanwhile, there was a reduction in DBP and MAP during bathing for TWI; however, DBP and MAP values returned to pre-bathing values immediately post-bathing. This demonstrated that HWI30 was a more time-efficient approach that elicited the same BP response as HWI60.
Chapter 5 investigated the acute CV response of HIIEx followed by HWI30 (ExHWI) versus HIIEx followed by TWI (ExTWI). There was a condition-by-time interaction effect for DBP, MAP, HR and Tc. ExHWI led to a greater hyperthermic and CV response than ExTWI, as shown by the greater elevated Tc and HR during bathing and immediately post-intervention. DBP and MAP were similarly reduced during bathing for ExHWI and ExTWI while only ExHWI saw a reduction in DBP and MAP immediately post-intervention. Therefore, ExHWI led to a greater hyperthermic response and lower BP response (immediately post-intervention) than ExTWI. ExHWI, HWI30, and HWI60 caused a robust CV response, including a hypotensive effect during bathing and immediately post-intervention in young, healthy adults. However, this effect was short-lasting, as blood pressure was restored by one-hour post-intervention and did not change 24 hours post-baseline. The thesis has revealed that despite the popularity of researchers using HWI60 within the literature, shorter HT protocols such as HWI30 can result in a similar hypotensive response during and immediately after bathing in young, healthy adults. Yet whether HWI30 or ExHWI can lead to long-term CV adaptations in young, healthy adults is yet to be determined
Research on the development of highspeed railway impact on the local economy
Get PDFHigh-speed railway(HSR) as a competitive intercity transport solution in areas of high population density have been constructed rapidly in the last decade. Due to the expensive construction and maintenance costs, many researchers have discussed the high speed railway benefit and impact on local economic developments from different aspects by different methodologies. To assess and evaluate the effectiveness of the newly constructed highspeed railway, it is necessary to designate a transport-economy analysis framework. Among most of the research, accessibility measurements have been frequently mentioned and tested with various definitions, indicators, and processing methods for assessing traffic system utility. Traditional accessibility measurement methods are diverse, but due to different scholars having their own distinct definitions, calculation methods, and application processes for accessibility, the resulting indices are difficult to compare and often lack practical significance. This presents challenges for city planners and transportation system designers when adopting specific indicators. Additionally, in the analysis of economic and trade issues, there is a lack of a unified approach for linking accessibility with specific economic statistical variables and applying them in real-world contexts. This limits the broader application of accessibility in various fields.
To improve the accessibility measurement and application, an analysis framework with an improved method of accessibility measurement based on travellers’ profitability is introduced in this research. Three levels of accessibility indicators, Daily Commuting Accessibility (DACC), Daily Work Commuting Accessibility (DWACC), and Weekly Return Accessibility (WACC) were designed based on different commuting frequencies and purposes. The average traveller’s income and local living cost were integrated to simulate the real commute scenario and assess the status of the transport system. In the case study, a series of statistics, containing 50 lines of travelling data and 11 years of economic data, was collected from the historical railway service record and local economy yearbook, in an area with 11 cities connected by conventional normal-speed and upgraded high-speed railway networks in the east of China. The index sheets measuring the three levels of accessibility indicated the changes in the travel benefit ratio throughout the test period following the popularisation of the high-speed railway service.
To validate the practicability of the new accessibility system, four empirical analyses, including the Optimal Intercity Traffic Service Speed analysis, Population Accessibility analysis, Dynamic Population Accessibility analysis and Industry Accessibility analysis were implemented. The first case, Optimal Intercity Traffic Service Speed analysis, discussed the travellers’ benefit level under different intercity railway service speeds. A series of accessibility values were estimated according to the service speed from conventional train service to the faster Maglev. The results indicated how the average traveller benefited from the faster service speed, stable journey cost and economic development. The second case introduced the local demographic data into the panel data regression model to illustrate the population migration impacted by the high-speed railway service. In the result, Daily Accessibility Coefficient (DACC) showed a negative impact on the registered population difference (RPD) with a coefficient of -1.281, indicating that high-speed rail services help to balance population distribution between departure and destination cities. In contrast, conventional rail services, represented by the Weekly Accessibility Coefficient (WACC), had a positive effect on RPD, with a coefficient of 0.3839, suggesting that conventional rail services tend to increase population disparities, proving that the high-speed railway service is more effective in reducing population aggregation than the conventional railway service. The high-speed railway service could help to rebalance the local uneven population distribution and promote the progress of urbanisation. The third case, Dynamic Population-Accessibility Effectiveness analysis, extended the second case to discuss the impact cycle and period of a newly operated service. The result showed an average of 4 to 5 years’ fluctuation in population migration and a hypothesis of urbanisation progress based on accessibility testing results was proposed. The last case analysed the relationship between the development of three sectors of the economy and intercity railway line construction. The tertiary and secondary sectors exhibited greater sensitivity to changes in traffic conditions, indicating that the more advanced industries in the economy have a higher demand for speed in intercity commuting. Even inside each group, the high-speed railway service presented a higher influence and stronger relationship on the industry development than the normal-speed railway service.
This study makes several key contributions to the field of transportation economics and regional development. By introducing a new accessibility measurement framework, it offers a practical tool for assessing the economic benefits of high-speed railway systems. The empirical analysis of the East China HSR network demonstrates how enhanced accessibility can improve economic integration, population mobility, and industrial growth, particularly in developing cities. The study also highlights the limitations of current HSR systems in terms of cost-effectiveness for daily commuters. The findings provide valuable insights for policymakers and urban planners, suggesting that while HSR drives regional development, careful planning is required to maximise its economic potential and ensure long-term sustainability
In situ sensing of multiple parameters for multi-functional adhesives
Get PDFOptical fibre sensors (OFS) have been widely recognised for their effectiveness in monitoring processes associated with epoxy-based polymers. Building on this foundation, this research expands the application of OFS to adhesive joints, facilitating in situ monitoring during manufacturing. This approach provides a robust and comprehensive means of ensuring bond quality and performance.
The study centres on fabricating single-lap joints (SLJs) using aluminium-to-aluminium, composite-to-composite, and aluminium-to-composite configurations. These joints were produced under varying surface preparation conditions, including different grit-blasting durations and silane concentrations, to assess their effects on bond strength and joint performance. Additionally, the integration of advanced sensor technologies, such as Fourier transform infrared spectroscopy (FTIR), fibre Bragg gratings (FBGs), Fresnel reflection sensors (FRS), and Fabry-Perot (FP) cavities, enabled the monitoring of critical parameters, including refractive index evolution, functional group changes, temperature, and shrinkage.
A comparative analysis of cure kinetics measured by FTIR and FRS demonstrated that FRS offers a cost-effective alternative to FTIR for monitoring the cure kinetics. The quantitative correlation of data between these methods reinforces the reliability of FRS for real-time monitoring applications. Furthermore, embedding multiple sensor types within SLJs provided valuable insights into the curing dynamics and performance of adhesive joints across diverse conditions. Additionally, a relation between FRS noise and viscosity could be established by comparing parallel rheology results with the noise thresholds of the FRS traces.
Key findings reveal that higher concentrations of silane treatments significantly reduce the ultimate tensile strength (UTS) of grit-blasted CFRP joints while not significantly improving aluminium joints. Additionally, surface roughness was found to correlate with the formation of microvoids in adhesive layers; increased roughness led to a higher density of voids, potentially compromising bond integrity. These results emphasise the critical role of precise surface preparation in achieving durable adhesive bonds.
This research demonstrates the capability of OFS to enable in situ monitoring of key parameters, such as refractive index, temperature, shrinkage, and chemical changes in functional groups. Furthermore, the successful integration of these sensors highlights their potential for both real-time process monitoring and post-process evaluations, advancing the development of smarter adhesive joint technologies for a wide range of engineering applications
Mathematical modelling of hydrocortisone replacement therapy
Get PDFCortisol is a stress hormone produced by the adrenal glands and is responsible for multiple processes in the body, including regulating blood pressure and sugar and managing the sleep/wake cycle. Adrenal insufficiency is a condition characterised by inadequate production of cortisol resulting in symptoms such as fatigue, weakness, and weight loss.
Hormone replacement therapy attempts to artificially regulate cortisol for patients with adrenal insufficiency, however this treatment is rarely personalised to an individual. In this thesis we develop mathematical models to predict hormone dynamics after the delivery of hydrocortisone (the term for cortisol delivered as a medication). We apply these models to assess differences in cortisol response after two commonly used delivery methods, namely a continuous intravenous infusion regime (CIV), and regular intravenous bolus injections (BIV). We fit these models to published experimental data from an in-patient study.
Driven by the desire to study the most parsimonious model that contains the dominant processes affecting blood cortisol levels, the models consider the substantial role of binding protein in changing cortisol dynamics, as well as its effects on excretion. For simplicity, other metabolic processes and distribution across physiological compartments (such as organs or tissues) are neglected. The resulting models comprise five free parameters common to both delivery modes. Additionally, by exploiting the disparity of time scales in the system we obtain asymptotically reduced models of each delivery mode, involving just four free parameters.
One critically important (but often neglected) aspect of models of this type is the desire to recover unique parameter values upon fitting to experimental data. We assess both the structural and practical identifiability of the derived models, highlighting those parameters which can be reliably inferred and those which cannot. We find that the models are practically identifiable for all model parameters except the binding and unbinding rates. This limitation is mitigated by the relative lack of sensitivity of cortisol dynamics to the precise value of these rates; instead it is the ratio of binding versus unbinding that governs dynamics. In all cases (except in the addition of significant noise) this ratio is shown to be practically recoverable. We further consider the question of whether low time-resolution measurements of combined concentrations of free and bound circulating cortisol enable model parameters to be uniquely estimated and/or inferred.
Finally, the models are fitted using both frequentist and Bayesian approaches, the latter having the added benefit of providing estimates regarding the uncertainty in the parameters which affect the dynamics. Parameter estimates from fitting the BIV model alone, and both BIV and CIV models simultaneously show good agreement, but differ from fitting only the CIV model. These differences highlight the advantage of integrating data from multiple modes of delivery to extract the dominant mechanisms of cortisol response thereby offering the potential to tailor treatments specific to an individual patient
Councillors' perceptions of audit committees: a strong structuration analysis
Get PDFThis thesis explores how councillors in English local councils perceive audit committees and the impact of those perceptions on the audit committee’s governance and accountability roles, analysed through Quadripartite Strong Structuration Theory (Stones, 2005).
Audit committees are not compulsory in England other than in Mayoral authorities but most councils have one and, while there is a considerable volume of research relating to audit committees particularly in the private sector, studies of councillors’ perceptions of them and the impacts of those perceptions on the governance and accountability roles of audit committees within the specific context of English local councils are very limited. It is this gap that this research aims to reduce.
Assuming a phenomenological approach and underpinned by Quadripartite Strong Structuration Theory (Q.S.S.T.), data were collected through minimally structured interviews with 24 councillors who were members of their councils' audit committees or, recent members, at the time of the interviews.
Using the quadripartite structure of Q.S.S.T. as the analytical framework, analysis of the interviews revealed three themes: 'The Cinderella Committee,' 'The Schleswig-Holstein Question' and 'The Party Hat.' 'The Cinderella Committee' reveals a general dispositional framework in which audit committees are perceived as mundane and low priority, leading to avoidance behaviours among councillors. ' The Schleswig-Holstein Question' uncovers the challenges councillors face in understanding complex financial reports and the perceived inadequacy of training, which constrains the ability to question effectively. ' The Party Hat' exposes the influence of political allegiances on audit committee independence and effectiveness, revealing conflicts of interest and the need for personal resilience among councillors in fulfilling their audit committee roles. The interview data suggest that, while some councillors recognise the importance of audit committees, negative perceptions and partisan influences often hinder the audit committee’s capacity to fulfil its governance and accountability roles effectively.
Against this backdrop of negativity, some interviewees, perceiving a conflict between their prior knowledge of audit committees and their current council experience, exercised their active agency to change negative attitudes and improve the independence and competence of the audit committee through positive messaging, changing the audit chair where that was perceived to be a political appointment and organising training and mentoring. These measures were effective but could be disrupted by changes in political leadership or control. Interviewees in opposition felt constrained by political structures from attempting to make changes.
This study concludes that the consistency of the narrative between interviewees from various councils provides evidence that councillors' perceptions of audit committees shape their engagement, competence, and independence which directly impacts the committee's effectiveness in fulfilling its governance and accountability roles.
These perceptions reveal challenges and weaknesses within local council audit committees but the insights gained may assist in the development of policies to enhance financial governance and accountability in English local councils
Development of advanced micro-nanotopological platforms for point-of-care diagnostics
Get PDFTopologically designed nano- and micro-structures have emerged as powerful tools for enhancing the detection of trace molecules in point-of-care (P-o-C) diagnostic devices, particularly for diseases such as traumatic brain injury (TBI). These structures, often fabricated using photolithography that includes photoresists on silicon wafers, offer precise control over certain parameters and significantly improve the detection of low-concentration biomarkers.
A key application of these structures is surface-enhanced Raman scattering (SERS), which amplifies the Raman signals by several orders of magnitude. By carefully designing the topology of metal-coated structures, it is possible to create highly localised electric fields that enhance the
Raman scattering of molecules adsorbed on their surfaces. This enables the detection of trace biomarkers, providing early diagnosis and intervention for conditions such as TBI.
The research presented here explores the optimisation of topological nano- and micro-structures via photolithography to maximise SERS signal enhancement. By analysing various design parameters, including the shape, size, and arrangement of structures, optimal configurations were
identified, which led to significant improvements in the detection of benzenethiol molecules and some TBI biomarkers. The impact of different metallic coatings, such as gold and silver, on SERS performance and the choice of laser wavelength to obtain high-quality Raman spectra was
investigated.
The developed structures have the potential to revolutionise P-o-C diagnostics by enabling rapid, accurate, and sensitive detection of a wide range of biomarkers. This rapid fabrication method using photolithography holds promise for improving healthcare outcomes and facilitating early
intervention in various diseases, including TBI
Investigating the homeostatic role and biomedical implications of the autophagy–NAD axis using human pluripotent stem cell-based platforms
Get PDFAutophagy is a homeostatic process critical for cell survival and human health. It is an intracellular degradative process that removes undesirable macromolecules (like protein aggregates) and damaged organelles (like mitochondria) from the cells. Due to the vital role of autophagy in maintaining cellular homeostasis, malfunction of this process contributes to cell death and tissue degeneration. This is particularly detrimental for post-mitotic cells like neurons. Indeed, dysfunction of autophagy has been implicated in diverse human pathological conditions including a range of neurodegenerative diseases. However, the mechanistic understanding of how impairment in autophagy contributes to cell death remains elusive. Elucidating the cytotoxic mechanism will be of biomedical interest for developing therapeutic interventions to combat neurodegeneration.
To undertake human-relevant biology in physiological and preclinical in vitro experimental platforms, human embryonic stem cells (hESCs) and human induced pluripotent stem cells (iPSCs) were utilised in this study to generate neuronal cells. A genetic hESC model with autophagy knockout (ATG5−/−) was used for generating human neurons with autophagy deficiency in order to study how loss of autophagy affects neuronal survival. Autophagy-deficient hESCs and hESC-derived neurons exhibited higher cell death at basal level accompanied by metabolic defects. Depletion of a metabolite called nicotinamide adenine dinucleotide (NAD) due to hyperactivation of NAD-consuming enzymes, such as SIRTs and PARPs, was found to trigger cell death via mitochondrial depolarisation in ATG5−/− hESC-derived neurons. Elevating intracellular NAD levels by supplementation with NAD precursors promoted the survival of ATG5−/− hESC-derived neurons by restoring mitochondrial bioenergetics and proteostasis. These findings elucidate a mechanistic link between autophagy deficiency and neuronal cell death that can be targeted for therapeutic interventions in neurodegenerative diseases associated with autophagic defects.
The biomedical relevance of this mechanism was further investigated in patient-derived iPSC model of a rare, early-onset neurodegenerative disease called Wolfram syndrome (WS). WS patient iPSC-derived neurons exhibited higher cell death that was associated with defective autophagy and NAD depletion, along with mitochondrial dysfunction and impairment in proteostasis. Targeting the defective autophagy–NAD axis in WS by autophagy and NAD enhancers ameliorated these disease phenotypes and improved the survival of WS patient iPSC-derived neurons, thereby highlighting a potential therapeutic strategy for the treatment of WS.
For future clinical translation by drug repurposing, a human neuronal platform was established using an autophagy reporter (mCherry-EGFP-LC3) hESC line in order to identify FDA-approved, CNS-penetrant, autophagy-inducing drugs via image-based chemical screen. Based on the efficacy in inducing autophagy at clinically-relevant dose, paediatric use, oral deliverability, and mTOR independence, four high-confidence hits were selected that include carbamazepine, nimodipine, sodium valproate and verapamil. All these FDA-approved autophagy inducers were shown to rescue disease phenotypes and improve cell survival in WS patient iPSC-derived neurons, thus informing potential drug candidates for clinical trials in future.
In a nutshell, defective autophagy–NAD axis was found to contribute to neuronal cell death, whilst targeting this cytotoxic cascade by autophagy and NAD enhancers exerted therapeutic benefits in patient-derived neuronal cells of a rare neurodegenerative disease. Since many rare and common neurodegenerative conditions are associated with autophagy dysfunction and NAD depletion, the findings from this work has the potential to be generalisable to some of these disease contexts
Interplay between migraine and pregnancy outcomes
Get PDFBackground: Migraine is highly prevalent in women of reproductive age and there is evidence to suggest that it impacts on the risk of adverse pregnancy outcomes. In particular, an association between migraine and pre-eclampsia has been well described. Links between migraine and other pregnancy outcomes such as miscarriage and preterm birth have been investigated, but findings have been less conclusive. Migraine often requires pharmacological therapy to manage symptoms and prevent episodes, but information about the safety of some migraine medication during pregnancy is lacking. This thesis aims to describe the epidemiology of migraine in pregnancy, determine its associated outcomes, and assess the safety of migraine medication during pregnancy.
Methods: An epidemiological study was carried out using and electronic primary care record database to describe the annual prevalence of migraine in pregnancy and the medications commonly prescribed amongst pregnant women with migraine. An umbrella review was conducted of literature comparing pregnancy outcomes in i) women with migraine to women without migraine ii) women with migraine who were treated to women with migraine who were not treated during pregnancy. A retrospective matched cohort study using the CPRD pregnancy register was conducted to compare the risk of miscarriage in women with migraine to those without migraine. Within the migraine cohort, a nested case-control study was conducted to compare the odds of miscarriage in those exposed to migraine medication in pregnancy compared to women with migraine who were not exposed to medication. Finally, a retrospective cohort study using delivery records from the Hospital Episode Statistics (HES) maternity tail was conducted to compare delivery outcomes (preterm birth, low birth weight, small for gestational age, mode of delivery and stillbirth) in women with migraine to those without migraine.
Results: The age-adjusted prevalence of migraine in pregnancy increased from 11.4% (95% CI 10.3%-12.4%) in 2000 to 17.2% (95% CI 16.7%-17.5%) in 2018. Over the same period, there was an increase in the rates of prescription for numerous medications for the management of migraine, notably, triptans, antidepressants (including amitriptyline) and beta blockers. In the umbrella review, migraine was associated with a higher odds of pre-eclampsia (pooled OR 2.05 (1.47-2.84), peripartum mental illness (pooled OR = 1.75 (1.20-2.54)) and preterm birth (pooled OR 1.26 (1.21-1.32)). Triptan-exposed women had increased odds of miscarriage compared to women without migraine (pooled OR 3.54 (2.24-5.59)). In the matched cohort study, migraine was associated with a 6% higher risk of miscarriage (aRR 1.06 95% CI (1.04-1.08)). Results from the nested case-control study showed that in pregnancies of women with migraine, exposure to triptans, amitriptyline and NSAIDs were associated with a significantly higher odds of miscarriage (aORs 1.24 (1.11-1.38), 1.25 (1.08-1.45) and 1.74 (1.57-1.93), respectively). Migraine was associated with an higher risk of extremely preterm (aRR 1.18 (95% CI 1.01-1.37) and medically-indicated preterm delivery (aRR 1.11 (95% CI 1.02-1.20)) in the matched delivery record cohort.
Conclusion: Prevalence of recorded migraine during pregnancy has increased over the past few decades, as have rates of prescriptions for migraine medications during pregnancy. Migraine was associated with pregnancy complications such as pre-eclampsia, peripartum mental illness, miscarriage and preterm birth (potentially driven by medically indicated preterm birth). Exposure to triptans, NSAIDs and amitriptyline in pregnant women with migraine was associated with miscarriage. Future work should focus on how migraine type and severity impact these outcomes, the associations of migraine drugs with other pregnancy outcomes and potential underlying causative mechanisms
Preservation of determinism in MBQC under ZX-calculus rewrites
Get PDFThe ZX-calculus is a powerful graphical language for reasoning about and optimizing quantum computations, being able to represent and rewrite both quantum circuits and measurement-based quantum computations (MBQCs) in a natural way, along with acting as a tool to translate between the two aforementioned types of quantum computation. Finding a circuit that is equivalent to a ZX-diagram can be #P hard [11] - it is therefore
important to look at the classes of ZX-diagrams that we have efficient circuit extraction algorithms for. The most general of these classes are ZX-diagrams with a property known as Pauli flow - this is a property from measurement-based quantum computing which ensures that computations remain deterministic despite quantum measurements being inherently probabilistic. The standard ZX-calculus rules are not particularly well suited
to measurement-based quantum computing as they often do not preserve the existence of Pauli flow nor preserve the MBQC structure itself. Thus by developing our understanding of ZX-calculus rewrite rules which preserve the existence of Pauli flow, we can better understand which ZX diagrams we are able to efficiently extract a circuit from as well as which Measurement-based computations we can perform deterministically.
In this thesis, I introduce new ZX-calculus rewrite rules and prove that these rules preserve the existence of Pauli flow. These rules have a variety of applications across many areas of quantum computation which will also be explored - to start, I show that these rules give us a procedure for rewriting any measurement-based quantum computation with arbitrary planar measurements along with X, Y and Z Pauli measurements into a diagram containing only XY -planar measurements and X and Y Pauli measurements (that is, only containing green spiders in the ZX-calculus). I then show that when we restrict to the stabilizer fragment of quantum computing - where we only have Pauli-measurements in measurement-based quantum computations - we are able to find a complete set of rewrite rules which preserve the existence of Pauli flow. To do this, I introduce a procedure for rewriting any stabilizer ZX-diagram into a unique normal form using only flow-preserving rewrite rules.
Finally, I examine the flow preservation of the "neighbour unfusion" rule of [60]. This rule was used in an optimization procedure for reducing 2-qubit gate count but the authors did not know in what cases this rule preserved gflow which was important for their algorithm to function. Neighbour unfusion is a special case of one of the rules which I proved to preserve Pauli flow and so it also preserves Pauli flow, but it is not as simple in the case of gflow. I find a condition that is both sufficient and necessary for neighbour unfusion to preserve the existence of gflow, along with providing less strict conditions for gflow to be preserved that can function as useful heuristics in their algorithm
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