Generalized methods and solvers for noise removal from piecewise constant signals. I. Background theory

Removing noise from piecewise constant (PWC) signals is a challenging signal processing problem arising in many practical contexts. For example, in exploration geosciences, noisy drill hole records need to be separated into stratigraphic zones, and in biophysics, jumps between molecular dwell states have to be extracted from noisy fluorescence microscopy signals. Many PWC denoising methods exist, including total variation regularization, mean shift clustering, stepwise jump placement, running medians, convex clustering shrinkage and bilateral filtering; conventional linear signal processing methods are fundamentally unsuited. This paper (part I, the first of two) shows that most of these methods are associated with a special case of a generalized functional, minimized to achieve PWC denoising. The minimizer can be obtained by diverse solver algorithms, including stepwise jump placement, convex programming, finite differences, iterated running medians, least angle regression, regularization path following and coordinate descent. In the second paper, part II, we introduce novel PWC denoising methods, and comparisons between these methods performed on synthetic and real signals, showing that the new understanding of the problem gained in part I leads to new methods that have a useful role to play.

Ash control methods to limit biomass inorganic content and its effect on fast pyrolysis bio-oil stability

This research investigates specific ash control methods to limit inorganic content within biomass prior to fast pyrolysis and effect of specific ash components on fast pyrolysis processing, mass balance yields and bio-oil quality and stability. Inorganic content in miscanthus was naturally reduced over the winter period from June (7.36 wt. %) to February (2.80 wt. %) due to a combination of senescence and natural leaching from rain water. September harvest produced similar mass balance yields, bio-oil quality and stability compared to February harvest (conventional harvest), but nitrogen content in above ground crop was to high (208 kg ha.-1) to maintain sustainable crop production. Deionised water, 1.00% HCl and 0.10% Triton X-100 washes were used to reduce inorganic content of miscanthus. Miscanthus washed with 0.10% Triton X-100 resulted in the highest total liquid yield (76.21 wt. %) and lowest char and reaction water yields (9.77 wt. % and 8.25 wt. % respectively). Concentrations of Triton X-100 were varied to study further effects on mass balance yields and bio-oil stability. All concentrations of Triton X-100 increased total liquid yield and decreased char and reaction water yields compared to untreated miscanthus. In terms of bio-oil stability 1.00% Triton X-100 produced the most stable bio-oil with lowest viscosity index (2.43) and lowest water content index (1.01). Beech wood was impregnated with potassium and phosphorus resulting in lower liquid yields and increased char and gas yields due to their catalytic effect on fast pyrolysis product distribution. Increased potassium and phosphorus concentrations produced less stable bio-oils with viscosity and water content indexes increasing. Fast pyrolysis processing of phosphorus impregnated beech wood was problematic as the reactor bed material agglomerated into large clumps due to char formation within the reactor, affecting fluidisation and heat transfer.

Optical quality for keratoconic eyes with conventional RGP lens and simulated, customised contact lens corrections:a comparison

Purpose: To compare monochromatic aberrations of keratoconic eyes when uncorrected, corrected with spherically-powered RGP (rigid gas-permeable) contact lenses and corrected using simulations of customised soft contact lenses for different magnitudes of rotation (up to 15°) and translation (up to 1mm) from their ideal position. Methods: The ocular aberrations of examples of mild, moderate and severe keratoconic eyes were measured when uncorrected and when wearing their habitual RGP lenses. Residual aberrations and point-spread functions of each eye were simulated using an ideal, customised soft contact lens (designed to neutralise higher-order aberrations, HOA) were calculated as a function of the angle of rotation of the lens from its ideal orientation, and its horizontal and vertical translation. Results: In agreement with the results of other authors, the RGP lenses markedly reduced both lower-order aberrations and HOA for all three patients. When compared with the RGP lens corrections, the customised lens simulations only provided optical improvements if their movements were constrained within limits which appear to be difficult to achieve with current technologies. Conclusions: At the present time, customised contact lens corrections appear likely to offer, at best, only minor optical improvements over RGP lenses for patients with keratoconus. If made in soft materials, however, these lenses may be preferred by patients in term of comfort. © 2012 The College of Optometrists.

Comparison between conventional and stochastic pinning control

Theoretical developments on pinning control of complex dynamical networks have mainly focused on the deterministic versions of the model dynamics. However, the dynamical behavior of most real networks is often affected by stochastic noise components. In this paper the pinning control of a stochastic version of the coupled map lattice network with spatiotemporal characteristics is studied. The control of these complex dynamical networks have functional uncertainty which should be considered when calculating stabilizing control signals. Two feedback control methods are considered: the conventional feedback control and modified stochastic feedback control. It is shown that the typically-used conventional control method suffers from the ignorance of model uncertainty leading to a reduction and potentially a collapse in the control efficiency. Numerical verification of the main result is provided for a chaotic coupled map lattice network. © 2011 IEEE.

Free radical reaction products and antioxidant capacity in beating heart coronary artery surgery compared to conventional bypass

Oxygen-derived free radicals are important agents of tissue injury during ischemia and reperfusion. The aim of this study was to investigate changes in protein and lipid oxidation and antioxidant status in beating heart coronary artery surgery and conventional bypass and to compare oxidative stress parameters between the two bypass methods. Serum lipid hydroperoxide, nitric oxide, protein carbonyl, nitrotyrosine, vitamin E, and β-carotene levels and total antioxidant capacity were measured in blood of 30 patients undergoing beating heart coronary artery surgery (OPCAB, off-pump coronary artery bypass grafting) and 12 patients undergoing conventional bypass (CABG, on-pump coronary artery bypass grafting). In the OPCAB group, nitric oxide and nitrotyrosine levels decreased after reperfusion. Similarly, β-carotene level and total antioxidant capacity also decreased after anesthesia and reperfusion. In the CABG group, nitric oxide and nitrotyrosine levels decreased after ischemia and reperfusion. However, protein carbonyl levels elevated after ischemia and reperfusion. Vitamin E, β-carotene, and total antioxidant capacity decreased after ischemia and reperfusion. Significantly decreased nitration and impaired antioxidant status were seen after reperfusion in both groups. Moreover, elevated protein carbonyls were found in the CABG group. The off-pump procedure is associated with lower degree of oxidative stress than on-pump coronary surgery. © 2011 Pleiades Publishing, Ltd.

Improved estimation of postmortem interval with Cardiac Troponin T and improved analytical methods

Accurate knowledge of the time since death, or postmortem interval (PMI), has enormous legal, criminological, and psychological impact. In this study, an investigation was made to determine whether the relationship between the degradation of the human cardiac structure protein Cardiac Troponin T and PMI could be used as an indicator of time since death, thus providing a rapid, high resolution, sensitive, and automated methodology for the determination of PMI. ^ The use of Cardiac Troponin T (cTnT), a protein found in heart tissue, as a selective marker for cardiac muscle damage has shown great promise in the determination of PMI. An optimized conventional immunoassay method was developed to quantify intact and fragmented cTnT. A small sample of cardiac tissue, which is less affected than other tissues by external factors, was taken, homogenized, extracted with magnetic microparticles, separated by SDS-PAGE, and visualized with Western blot by probing with monoclonal antibody against cTnT. This step was followed by labeling and available scanners. This conventional immunoassay provides a proper detection and quantitation of cTnT protein in cardiac tissue as a complex matrix; however, this method does not provide the analyst with immediate results. Therefore, a competitive separation method using capillary electrophoresis with laser-induced fluorescence (CE-LIF) was developed to study the interaction between human cTnT protein and monoclonal anti-TroponinT antibody. ^ Analysis of the results revealed a linear relationship between the percent of degraded cTnT and the log of the PMI, indicating that intact cTnT could be detected in human heart tissue up to 10 days postmortem at room temperature and beyond two weeks at 4C. The data presented demonstrates that this technique can provide an extended time range during which PMI can be more accurately estimated as compared to currently used methods. The data demonstrates that this technique represents a major advance in time of death determination through a fast and reliable, semi-quantitative measurement of a biochemical marker from an organ protected from outside factors. ^

Clean hydrogen production and carbon dioxide capture methods

Fossil fuels constitute a significant fraction of the world's energy demand. The burning of fossil fuels emits huge amounts of carbon dioxide into the atmosphere. Therefore, the limited availability of fossil fuel resources and the environmental impact of their use require a change to alternative energy sources or carriers (such as hydrogen) in the foreseeable future. The development of methods to mitigate carbon dioxide emission into the atmosphere is equally important. Hence, extensive research has been carried out on the development of cost-effective technologies for carbon dioxide capture and techniques to establish hydrogen economy. Hydrogen is a clean energy fuel with a very high specific energy content of about 120MJ/kg and an energy density of 10Wh/kg. However, its potential is limited by the lack of environment-friendly production methods and a suitable storage medium. Conventional hydrogen production methods such as Steam-methane-reformation and Coal-gasification were modified by the inclusion of NaOH. The modified methods are thermodynamically more favorable and can be regarded as near-zero emission production routes. Further, suitable catalysts were employed to accelerate the proposed NaOH-assisted reactions and a relation between reaction yield and catalyst size has been established. A 1:1:1 molar mixture of LiAlH 4, NaNH2 and MgH2 were investigated as a potential hydrogen storage medium. The hydrogen desorption mechanism was explored using in-situ XRD and Raman Spectroscopy. Mesoporous metal oxides were assessed for CO2 capture at both power and non-power sectors. A 96.96% of mesoporous MgO (325 mesh size, surface area = 95.08 ± 1.5 m2/g) was converted to MgCO 3 at 350°C and 10 bars CO2. But the absorption capacity of 1h ball milled zinc oxide was low, 0.198 gCO2 /gZnO at 75°C and 10 bars CO2. Interestingly, 57% mass conversion of Fe and Fe 3O4 mixture to FeCO3 was observed at 200°C and 10 bars CO2. MgO, ZnO and Fe3O4 could be completely regenerated at 550°C, 250°C and 350°C respectively. Furthermore, the possible retrofit of MgO and a mixture of Fe and Fe3O 4 to a 300 MWe coal-fired power plant and iron making industry were also evaluated.

A study of methods used to analyze total oil and polycyclic aromatic hydrocarbons in produced water: steps towards the validation of molecularly imprinted polymers for use in marine environmetns

Produced water is a by-product of offshore oil and gas production, and is released in large volumes when platforms are actively processing crude oil. Some pollutants are not typically removed by conventional oil/water separation methods and are discharged with produced water. Oil and grease can be found dispersed in produced water in the form of tiny droplets, and polycyclic aromatic hydrocarbons (PAHs) are commonly found dissolved in produced water. Both can have acute and chronic toxic effects in marine environments even at low exposure levels. The analysis of the dissolved and dispersed phases are a priority, but effort is required to meet the necessary detection limits. There are several methods for the analysis of produced water for dispersed oil and dissolved PAHs, all of which have advantages and disadvantages. In this work, EPA Method 1664 and APHA Method 5520 C for the determination of oil and grease will be examined and compared. For the detection of PAHs, EPA Method 525 and PAH MIPs will be compared, and results evaluated. APHA Method 5520 C Partition-Infrared Method is a liquid-liquid extraction procedure with IR determination of oil and grease. For analysis on spiked samples of artificial seawater, extraction efficiency ranged from 85 – 97%. Linearity was achieved in the range of 5 – 500 mg/L. This is a single-wavelength method and is unsuitable for quantification of aromatics and other compounds that lack sp³-hybridized carbon atoms. EPA Method 1664 is the liquid-liquid extraction of oil and grease from water samples followed by gravimetric determination. When distilled water spiked with reference oil was extracted by this procedure, extraction efficiency ranged from 28.4 – 86.2%, and %RSD ranged from 7.68 – 38.0%. EPA Method 525 uses solid phase extraction with analysis by GC-MS, and was performed on distilled water and water from St. John’s Harbour, all spiked with naphthalene, fluorene, phenanthrene, and pyrene. The limits of detection in harbour water were 0.144, 3.82, 0.119, and 0.153 g/L respectively. Linearity was obtained in the range of 0.5-10 g/L, and %RSD ranged from 0.36% (fluorene) to 46% (pyrene). Molecularly imprinted polymers (MIPs) are sorbent materials made selective by polymerizing functional monomers and crosslinkers in the presence of a template molecule, usually the analytes of interest or related compounds. They can adsorb and concentrate PAHs from aqueous environments and are combined with methods of analysis including GC-MS, LC-UV-Vis, and desorption electrospray ionization (DESI)- MS. This work examines MIP-based methods as well as those methods previously mentioned which are currently used by the oil and gas industry and government environmental agencies. MIPs are shown to give results consistent with other methods, and are a low-cost alternative improving ease, throughput, and sensitivity. PAH MIPs were used to determine naphthalene spiked into ASTM artificial seawater, as well as produced water from an offshore oil and gas operation. Linearity was achieved in the range studied (0.5 – 5 mg/L) for both matrices, with R² = 0.936 for seawater and R² = 0.819 for produced water. The %RSD for seawater ranged from 6.58 – 50.5% and for produced water, from 8.19 – 79.6%.

Conventional versus hypofractionated high-dose intensity-modulated radiotherapy for prostate cancer: 5-year outcomes of the randomised, non-inferiority, phase 3 CHHiP trial

BACKGROUND: Prostate cancer might have high radiation-fraction sensitivity that would give a therapeutic advantage to hypofractionated treatment. We present a pre-planned analysis of the efficacy and side-effects of a randomised trial comparing conventional and hypofractionated radiotherapy after 5 years follow-up.

METHODS: CHHiP is a randomised, phase 3, non-inferiority trial that recruited men with localised prostate cancer (pT1b-T3aN0M0). Patients were randomly assigned (1:1:1) to conventional (74 Gy delivered in 37 fractions over 7·4 weeks) or one of two hypofractionated schedules (60 Gy in 20 fractions over 4 weeks or 57 Gy in 19 fractions over 3·8 weeks) all delivered with intensity-modulated techniques. Most patients were given radiotherapy with 3-6 months of neoadjuvant and concurrent androgen suppression. Randomisation was by computer-generated random permuted blocks, stratified by National Comprehensive Cancer Network (NCCN) risk group and radiotherapy treatment centre, and treatment allocation was not masked. The primary endpoint was time to biochemical or clinical failure; the critical hazard ratio (HR) for non-inferiority was 1·208. Analysis was by intention to treat. Long-term follow-up continues. The CHHiP trial is registered as an International Standard Randomised Controlled Trial, number ISRCTN97182923.

FINDINGS: Between Oct 18, 2002, and June 17, 2011, 3216 men were enrolled from 71 centres and randomly assigned (74 Gy group, 1065 patients; 60 Gy group, 1074 patients; 57 Gy group, 1077 patients). Median follow-up was 62·4 months (IQR 53·9-77·0). The proportion of patients who were biochemical or clinical failure free at 5 years was 88·3% (95% CI 86·0-90·2) in the 74 Gy group, 90·6% (88·5-92·3) in the 60 Gy group, and 85·9% (83·4-88·0) in the 57 Gy group. 60 Gy was non-inferior to 74 Gy (HR 0·84 [90% CI 0·68-1·03], pNI=0·0018) but non-inferiority could not be claimed for 57 Gy compared with 74 Gy (HR 1·20 [0·99-1·46], pNI=0·48). Long-term side-effects were similar in the hypofractionated groups compared with the conventional group. There were no significant differences in either the proportion or cumulative incidence of side-effects 5 years after treatment using three clinician-reported as well as patient-reported outcome measures. The estimated cumulative 5 year incidence of Radiation Therapy Oncology Group (RTOG) grade 2 or worse bowel and bladder adverse events was 13·7% (111 events) and 9·1% (66 events) in the 74 Gy group, 11·9% (105 events) and 11·7% (88 events) in the 60 Gy group, 11·3% (95 events) and 6·6% (57 events) in the 57 Gy group, respectively. No treatment-related deaths were reported.

INTERPRETATION: Hypofractionated radiotherapy using 60 Gy in 20 fractions is non-inferior to conventional fractionation using 74 Gy in 37 fractions and is recommended as a new standard of care for external-beam radiotherapy of localised prostate cancer.

FUNDING: Cancer Research UK, Department of Health, and the National Institute for Health Research Cancer Research Network.

Methods, Models & Systems for Dealing with Some Business, Management & Engineering Problems

This keynote presentation will report some of our research work and experience on the development and applications of relevant methods, models, systems and simulation techniques in support of different types and various levels of decision making for business, management and engineering. In particular, the following topics will be covered. Modelling, multi-agent-based simulation and analysis of the allocation management of carbon dioxide emission permits in China (Nanfeng Liu & Shuliang Li Agent-based simulation of the dynamic evolution of enterprise carbon assets (Yin Zeng & Shuliang Li) A framework & system for extracting and representing project knowledge contexts using topic models and dynamic knowledge maps: a big data perspective (Jin Xu, Zheng Li, Shuliang Li & Yanyan Zhang) Open innovation: intelligent model, social media & complex adaptive system simulation (Shuliang Li & Jim Zheng Li) A framework, model and software prototype for modelling and simulation for deshopping behaviour and how companies respond (Shawkat Rahman & Shuliang Li) Integrating multiple agents, simulation, knowledge bases and fuzzy logic for international marketing decision making (Shuliang Li & Jim Zheng Li) A Web-based hybrid intelligent system for combined conventional, digital, mobile, social media and mobile marketing strategy formulation (Shuliang Li & Jim Zheng Li) A hybrid intelligent model for Web & social media dynamics, and evolutionary and adaptive branding (Shuliang Li) A hybrid paradigm for modelling, simulation and analysis of brand virality in social media (Shuliang Li & Jim Zheng Li) Network configuration management: attack paradigms and architectures for computer network survivability (Tero Karvinen & Shuliang Li)

Reading comprehension of czech pupils at the beginning of primary school: comparison betweenanalytic-synthetic and genetic methods

In Czech schools two teaching methods of reading are used: the analytic-synthetic (conventional) and genetic (created in the 1990s). They differ in theoretical foundations and in methodology. The aim of this paper is to describe the above mentioned theoretical approaches and present the results of study that followed the differences in the development of initial reading skills between these methods. A total of 452 first grade children (age 6-8) were assessed by a battery of reading tests at the beginning and at the end of the first grade and at the beginning of the second grade. 350 pupils participated all three times. Based on data analysis the developmental dynamics of reading skills in both methods and the main differences in several aspects of reading abilities (e.g. the speed of reading, reading technique, error rate in reading) are described. The main focus is on the reading comprehension development. Results show that pupils instructed using genetic approach scored significantly better on used reading comprehension tests, especially in the first grade. Statistically significant differences occurred between classes independently of each method. Therefore, other factors such as teacher´s role and class composition are discussed.

Therapeutic Potential of RNAi Through Endocytotic Methods

The ability to manipulate gene expression promises to be an important tool for the management of infectious diseases and genetic disorders. However, a major limitation to effective delivery of therapeutic RNA to living cells is the cellular toxicity of conventional techniques. Team PANACEA’s research objective was to create new reagents based on a novel small-molecule delivery system that uses a modular recombinant protein vehicle consisting of a specific ligand coupled to a Hepatitis B Virus-derived RNA binding domain (HBV-RBD). Two such recombinant delivery proteins were developed: one composed of Interleukin-8, the other consisting of the Machupo Virus GP1 protein. The ability of these proteins to deliver RNA to cells were then tested. The non-toxic nature of this technology has the potential to overcome limitations of current methods and could provide a platform for the expansion of personalized medicine.

Advanced Adhesion Strength Testing Methods of Thin Film Multilayers in Electronic Packaging Systems

With the continued miniaturization and increasing performance of electronic devices, new technical challenges have arisen. One such issue is delamination occurring at critical interfaces inside the device. This major reliability issue can occur during the manufacturing process or during normal use of the device. Proper evaluation of the adhesion strength of critical interfaces early in the product development cycle can help reduce reliability issues and time-to-market of the product. However, conventional adhesion strength testing is inherently limited in the face of package miniaturization, which brings about further technical challenges to quantify design integrity and reliability. Although there are many different interfaces in today's advanced electronic packages, they can be generalized into two main categories: 1) rigid to rigid connections with a thin flexible polymeric layer in between, or 2) a thin film membrane on a rigid structure. Knowing that every technique has its own advantages and disadvantages, multiple testing methods must be enhanced and developed to be able to accommodate all the interfaces encountered for emerging electronic packaging technologies. For evaluating the adhesion strength of high adhesion strength interfaces in thin multilayer structures a novel adhesion test configuration called “single cantilever adhesion test (SCAT)” is proposed and implemented for an epoxy molding compound (EMC) and photo solder resist (PSR) interface. The test method is then shown to be capable of comparing and selecting the stronger of two potential EMC/PSR material sets. Additionally, a theoretical approach for establishing the applicable testing domain for a four-point bending test method was presented. For evaluating polymeric films on rigid substrates, major testing challenges are encountered for reducing testing scatter and for factoring in the potentially degrading effect of environmental conditioning on the material properties of the film. An advanced blister test with predefined area test method was developed that considers an elasto-plastic analytical solution and implemented for a conformal coating used to prevent tin whisker growth. The advanced blister testing with predefined area test method was then extended by employing a numerical method for evaluating the adhesion strength when the polymer’s film properties are unknown.

Manure and sorbent fertilisers increase on-going nutrient availability relative to conventional fertilisers

The key to better nutrient efficiency is to simultaneously improve uptake and decrease losses. This study sought to achieve this balance using sorbent additions and manure nutrients (spent poultry litter; SL) compared with results obtained using conventional sources (Conv; urea nitrogen, N; and phosphate–phosphorus; P). Two experiments were conducted. Firstly, a phosphorus pot trial involving two soils (sandy and clay) based on a factorial design (Digitaria eriantha/Pennisetum clandestinum). Subsequently, a factorial N and P field trial was conducted on the clay soil (D. eriantha/Lolium rigidum). In the pot trial, sorbent additions (26.2 g of hydrotalcite [HT] g P− 1) to the Conv treatment deferred P availability (both soils) as did SL in the sandy soil. In this soil, P delivery by the Conv treatments declined rapidly, and began to fall behind the HT and SL treatments. Addition of HT increased post-trial Colwell P. In the field trial low HT-rates (3.75 and 7.5 g of HT g P− 1) plus bentonite, allowed dry matter production and nutrient uptake to match that of Conv treatments, and increased residual mineral-N. The SL treatments performed similarly to (or better than) Conv treatments regarding nutrient uptake. With successive application, HT forms may provide better supply profiles than Conv treatments. Our findings, combined with previous studies, suggest it is possible to use manures and ion-exchangers to match conventional N and P source productivity with lower risk of nutrient losses.

Analysis of N-nitrosames in water using micellar electrokinetic chromatography (MEKC) and development of online and offline methods of extraction and enrichment of neutral polar analytes

Evaluation of the quality of the environment is essential for human wellness as pollutants in trace amounts can cause serious health problem. Nitrosamines are a group of compounds that are considered potential carcinogens and can be found in drinking water (as disinfection byproducts), foods, beverages and cosmetics. To monitor the level of these compounds to minimize daily intakes, fast and reliable analytical techniques are required. As these compounds are relatively highly polar, extraction and enrichment from environmental samples (aqueous) are challenging. Also, the trend of analytical techniques toward the reduction of sample size and minimization of organic solvent use demands new methods of analysis. In light of fulfilling these requirements, a new method of online preconcentration tailored to an electrokinetic chromatography is introduced. In this method, electroosmotic flow (EOF) was suppressed to increase the interaction time between analyte and micellar phase, therefore the only force to mobilize the neutral analytes is the interaction of analyte with moving micelles. In absence of EOF, polarity of applied potential was switched (negative or positive) to force (anionic or cationic) micelles to move toward the detector. To avoid the excessive band broadening due to longer analysis time caused by slow moving micelles, auxiliary pressure was introduced to boost the micelle movement toward the detector using an in house designed and built apparatus. Applying the external auxiliary pressure significantly reduced the analysis times without compromising separation efficiency. Parameters, such as type of surfactants, composition of background electrolyte (BGE), type of capillary, matrix effect, organic modifiers, etc., were evaluated in optimization of the method. The enrichment factors for targeted analytes were impressive, particularly; cationic surfactants were shown to be suitable for analysis of nitrosamines due to their ability to act as hydrogen bond donors. Ammonium perfluorooctanoate (APFO) also showed remarkable results in term of peak shapes and number of theoretical plates. It was shown that the separation results were best when a high conductivity sample was paired with a BGE of lower conductivity. Using higher surfactant concentrations (up to 200 mM SDS) than usual (50 mM SDS) for micellar electrokinetic chromatography (MEKC) improved the sweeping. A new method for micro-extraction and enrichment of highly polar neutral analytes (N-Nitrosamines in particular) based on three-phase drop micro-extraction was introduced and its performance studied. In this method, a new device using some easy-to-find components was fabricated and its operation and application demonstrated. Compared to conventional extraction methods (liquid-liquid extraction), consumption of organic solvents and operation times were significantly lower.