melanogaster. Fernandez and Klowden compared the hemolymph titers of Aea-HP-1 in gravid unmated and mated female A. aegypti using a radioimmunoassay [13]. The results suggested higher levels of Aea-HP-1 in the mated females, although the difference was not statistically significant and the identity of the immunoreactivity selleck kinase inhibitor was not confirmed by chromatography. Recently, a mass spectrometric study conducted by an expert group in the field of insect

neuropeptidomics compiled a comprehensive list of mature neuroendocrine peptides present in the central nervous system, neurohemal organs and various endocrine cells (including those of the mid-gut) of A. aegypti, but failed to detect Aea-HP-1 (or Aea-HP-3) in any of these tissues [34]. It is therefore not possible to pinpoint the source of Aea-HP-1 that was originally isolated from a large quantity of heads. These results taken together with the ease in which we detect Aea-HP-1 in a single MAG suggest that the male reproductive tissue is a major site of synthesis of this peptide, at least in adult males. None of the head peptides have been found in the peptidomes of other insects and genes coding for the head peptides have been notably absent from insect genome databases, even those of other

mosquitoes, suggesting a specific role for the peptide in Florfenicol reproduction of A. aegypti. Aea-HP-1 might fall into the category of male reproductive proteins which are subject to much faster evolutionary change compared to proteins MAPK inhibitor of non-reproductive tissues, possibly driven by sexual conflict [3]. Transplantation of MAGs, or injection of gland

extracts, into female A. aegypti can elicit a variety of post-mating responses including refractoriness to re-mating and inhibition of host-seeking and biting behavior [13]. We have not been able to show that Aea-HP-1 can induce mating rejection by injecting Aea-HP-1 (0.1–1 μg) into the hemocoel of virgin A. aegypti females (not presented). This failure might be due to lack of accessibility and the known rapid catabolism of Aea-HP-1 in the hemolymph [4]. D. melanogaster SP has wide-ranging effects on physiology and behavior some of which are mediated primarily through activation of the SP/MIP receptor that is expressed in sensory neurons of the uterus [42]. The D. melanogaster SP receptor and its A. aegypti orthologue are also strongly activated by myoinhibitory peptides (MIPs), a family of peptides that are found in species from different insect orders and are considered to be the ancestral ligands for these receptors [19], [33] and [41]. The receptors are also activated by unidentified ligands present in whole body extract of adult A. aegypti [19].

They also mention the successful use of protein adducts as biomarkers in the case of sulphur mustard, acrylamide, ethylene oxide, dichlorvos and acrylonitrile. Another example of the utility of biological monitoring was reported by Jones and

McCallum (2011). This involved a workplace ‘incident’ in which tunnelling workers were exposed to levels of benzene that exceeded exposure limits. Biological monitoring (urinary S-phenylmercapturic acid levels) revealed CHIR-99021 manufacturer high internal exposures to benzene despite the use of personal protection equipment Investigation showed this was due a combination of environmental and human factors. Improvements in protective equipment, work practices and worker behaviour led to significant reductions in exposure. Cyclopamine manufacturer For first responders to major incidents with no ‘normal’ exposure to the substance

and relying on personal protective equipment for control of exposure the more appropriate guidance values may be those derived from background/population levels. If the equipment is working and being used correctly it might be expected that systemic exposure will be low. However, in these cases and also for those potentially exposed in the wider population, care should be taken interpreting the results. Although population studies are very helpful in assessing the overall exposure of the population they are more difficult to interpret for the individual. Samples are usually collected at times

that are not defined in relation to exposure (extent or frequency) and may show considerable intra-individual variation (Aylward et al., 2014). Since biological monitoring guidance values for both environmental and for occupational exposures have their limitations in the aftermath of a chemical incident, there is a need for biological guidance values specific for use in such incidents. Biological guidance values help assess systemic exposure but are related to external exposure dose metrics. Acute Exposure Reference Values clonidine (AERVs) such as AEGLs (EPA, 2012) or Emergency Response Planning guidance Levels (ERPGs AIHA, 2013) are external exposure guidance values specifically derived for chemical incidents (Bos et al., 2013). This guidance can be used in support of the public health management of chemical incidents and should enable comparison of the public health impacts of the chemical exposure and of the possible emergency response measures such as shelter-in-place or evacuation. Such guidance values have at least three tiers (representing action levels) showing the following characteristics: 1. A threshold for discomfort or other minor, rapidly reversible health effects. The eldest programs for derivation of AERVs are the Emergency Response Planning Guidelines (ERPGs) and the Acute Exposure Guideline Levels (AEGLs), both initiated in the US.

Inflammation caused by Yersinia pseudotuberculosis increases the uptake of 100 nm carboxyl polystyrene particles in cell monolayers and in intestinal biopsies (Ragnarsson et al., 2008). In contrast to that, in the in vitro study by Leonhard et al. (2010) no influence on the translocation of the polystyrene

particles was selleck inhibitor observed. Since in the in vitro studies lipopolysaccharide and not intact bacteria were used, effects by the living bacteria on cells, mucus production and/or viscosity may account for the observed differences. The assessment of penetration and biological effects of ingested NMs presents many problems because it is very complex. Inter-individual differences in the composition, pH and thickness of the mucus layer, in the gastrointestinal flora and in gastrointestinal passage time complicate in vivo experiments. In the study of Loeschner et al. (2011) on organ distribution

of 60 nm Ag nanoparticles great inter-individual variations were noticed although all animals were fed the same diet. Also SB203580 differences in the diet are important. For in vivo testing, rodents also may not be ideal models. Although men and rodents are omnivorous, function (e.g., region for absorption of food) and morphology of the gastrointestinal tract (e.g., absence of gall bladder in rats) show considerable differences between rodents and humans (Kararli, 1995). Apart from permeating themselves, NMs may have permeation enhancing properties for other substances. This phenomenon

termed as ‘Trojan horse’ effect, was first identified for metal nanoparticles. Whereas plasma membranes restrict the cellular access for metal ions like silver cations, silver nanoparticles were readily internalized and intracellular silver concentrations were much higher than for silver ions (Navarro et al., 2008). Studies for uptake and toxicity should, therefore, include AgNO3 for silver nanoparticles (Trojan horse effect) or bulk material. Other important effects are linked to the tendency of NMs to absorb macromolecules. By adsorption of organic compounds also unintended molecules (undigested and unmetabolized compounds) may be absorbed by the gastrointestinal tract. On the other hand adsorption to NMs may also prevent the uptake of necessary molecules (Alkhamis et al., 2009). Absorption may also be altered by a changed metabolization Arachidonate 15-lipoxygenase by enterocytes. Polystyrene and silver particles have been shown to inhibit the activity of cytochrome P450 enzymes (Fröhlich et al., 2010 and Lamb et al., 2010). To obtain more information about penetration of the orogastrointestinal barriers and subsequent biological effects physiologically relevant in vitro models should be used, which enable the controlled variation of the most important parameters involved. Particle properties should be recorded in mucus of different pH and the extent of binding to proteins and other macromolecules should be studied.

White et al. reported on preliminary findings using a novel intra-operative brain-shift monitor using shear-mode transcranial ultrasound [16]. Despite the advantages of ultrasound in an intra-operative setting compared to other imaging methods [9], such as high temporal resolution, GPCR Compound Library portability, and non-ionizing mode of radiation, the application of commercially available TCS systems for intra-operative monitoring of DBS electrode placement has been reported only rarely so far. One early study applied a former-generation TCS system (Sonoline Elegra, Siemens; Erlangen, Germany) during implantation of DBS electrodes into the targeted subthalamic nucleus

(STN) in patients with Parkinson’s disease [17]. The authors reported an easy visualization of the 0.8 mm thick electrode. The position of the imaging artefact of the tip of the DBS electrode appeared to be within in the anatomic region of substantia nigra that usually is of high echogenicity in patients with Parkinson’s disease. Additionally, Selumetinib chemical structure the segment of the laterally

running posterior cerebral artery at the corresponding level could also be displayed. The authors found the appearing correct position of the DBS electrode tip on TCS at a place just touching the echo-signals of the substantia nigra. The results of this pilot study were limited by the poorer lateral image resolution of the TCS system applied compared to contemporary TCS systems [7], and the missing estimation of the exact size of the electrode imaging artifacts which caused some uncertainty with regard to the exact electrode tip position. In a more recent study, a contemporary

TCS system (Acuson Antares, Siemens; Erlangen, Germany) was applied intra-operatively to monitor the placement of DBS electrode into the GPI in patients with idiopathic dystonia [8]. In this study not only the visualization of the final DBS electrodes was possible but also the simultaneous visualization of 2–5 closely located microelectrodes used for detection of the optimal trajectory of the final electrode (Fig. 2A). Another advantage of the intra-operative TCS monitoring was that the distance of the DBS electrode tip to the artery at the anatomic Methamphetamine target (penetrating branch of the posterior communicating artery) could be assessed (Fig. 2B). This was possible since the extent of the imaging artefact of the electrode had been estimated in advance for the referring TCS system and implant [8]. This even enabled intra-operatively the decision to insert the final DBS electrode somewhat deeper than it would have been done using only the pre-operatively planned navigation data [8]. Simultaneous visualization of the artery at the anatomic target prevented hemorrhages at the target site.

The higher spatial resolution (250–500 m) and bigger spectral width (20 nm) of MODIS visual ‘land’ bands are very informative for the visual identification and analysis of turbid coastal water features

compared to the spectrally narrow (10 nm) and spatially less detailed (1 km) MODIS ‘ocean’ bands (Gurova 2009). However, for the spectral analysis of these features we used normalized water leaving radiances (nLw) (Gordon & Wang 1994) and spectral diffuse attenuation coefficients of downwelling irradiance Kd_Lee (Lee et al. 2005), calculated from the ‘ocean’ bands (8–16), specially designed for such purposes. Images were processed from L1A level with Seadas 6.23 software, using the MUMM atmospheric correction algorithm PD0325901 clinical trial (Ruddick et al. 2000), which is the best suited to turbid Baltic Sea waters (Woźniak et al. 2008). CDOM absorption coefficients aCDOM(400) were calculated using an empirical algorithm specially developed for the Baltic Sea and successfully validated ( Kowalczuk et al., 2005 and Kowalczuk et al., 2010). MODIS Sea Surface Temperature (SST) products were calculated with the standard algorithm implemented in Seadas 6.2 ( Brown & Minnett 1999). Wide Swath Mode images from Advanced Synthetic Aperture Radar (ASAR instrument on board the Envisat satellite)

were obtained from ESA archives. With a medium spatial resolution of 75 m pixel− 1, the ASAR WSM images, especially those obtained by multi-sensor approach, are very useful selleck screening library for detailed spatial analysis of hydrodynamic features affecting the water surface (Gurova & Ivanov 2011). Secondly, examples of submesoscale eddies in SEB were selected from a series of measurements of sea surface currents in the marine area near the Curonian Spit (the Zelenogradsk-Rybachiy section) and the northern shore of the Sambian Peninsula, made by the coastal radar Sea Sonde CODAR system in 2006 and 2007. Two resolutions for a 30 × 30-cell grid were used in these measurements – 500 m cell− 1 and 250 m cell− 1 (Gorbatsky et al., 2007 and Babakov

et al., 2008). To analyse the wind statistics we used wind data at altitude 10 m from a coupled Wilson disease protein sea-ice-ocean model of the Baltic Sea (BSIOM) with a spatial resolution of 1.2 nautical miles, which has been shown to provide realistic values when compared to field measurements (Rudolph & Lehmann 2006). Verification comparison of modelling data for a 6-hour average wind with measurements at point D6, located 20 km from the coast of the Curonian Spit, for a period of 92 days, showed general correspondence between the modelled data and measurements (Figure 2). Therefore, the wind statistics in this paper (Table 1 (see page 639) and wind diagrams in Figure 7 (see page 644)) were obtained using BSIOM data.

Cooking time is one of the traits evaluated by many breeding programs, and the Mattson Bean Cooker is the recommended equipment for measuring this variable (Proctor & Watts, 1987). In a standard Mattson analysis, soaked grains are positioned in each of the saddles of the rack so that the tip of each plunger is in contact with the surface of the grain. During the cooking test the lower portion of the cooker rack is immersed in a boiling water bath. When the grain becomes sufficiently tender, the plunger penetrates the grain and drops a short distance through the hole in the saddle. The time

this website at which a plunger drops is recorded manually (Wang & Daun, 2005). Instrumental texture analysis has been increasingly applied to assess the hardening of beans (Nasar-Abbas et al., 2008; Saha, Singh, Mahajan, & Gupta, 2009; Yousif, Deeth, Caffin, & Lisle, 2002), due to its characteristic of fast and practical execution, which enable its use to evaluate large number of genotypes in breeding program. However, the lack of standardization of sample preparation for this

type of analysis has resulted in quite divergent reports in the literature, making it difficult to compare the results. When the bean breeding program evaluates the grain resistance to cooking, it is necessary to adopt BGJ398 a method that is useful for distinguishing the differences in germplasm, conferring

high experimental accuracy and being representative of the cooking pattern that usually is achieved by consumers (Ribeiro, Cargnelutti Filho, Poersch, & Rosa, 2007). In this sense, more efficient and cost-effective methods of preparing and evaluating beans cooking quality would encourage the adoption of grain quality improvement as a focus of breeding programs and facilitate development of common beans’ cultivars with Exoribonuclease improved grain quality (Yeung et al., 2009). This work aimed to evaluate the effect of different practices for cooking fresh crop and aged dry beans on hardness and also to propose a procedure to prepare bean for instrumental texture analysis. Carioca beans (P. vulgaris L., cv Pérola) were provided by Embrapa Rice and Beans (Santo Antônio de Goiás, Brazil). The material was grown in two seasons at the same location (Capivara’s Farm, Santo Antônio de Goiás, Brazil). The first crop was harvested at the end of June 2011 and the second one at the beginning of October 2011. After harvest samples were naturally dried and sorted by hand to remove extremely small beans and those with defective seed coat or excessively dirty surfaces. Then each crop of carioca beans were packaged in polyethylene bags with a capacity of about 2 kg until the analysis.

0% and 6.9%, respectively (P < .01), and the procedure times per unit area of specimen were 4.7 and 11.9 min/cm2, respectively (P = .03). The median length of cancer extension was 3.0 mm (0.2-7.0 mm) in the BA group, and half of the cases with cancer extension were not detected by magnifying endoscopy before ESD. No significant differences in en bloc, complete, and LDK378 clinical trial curative resection rates were found between the BA and NB groups (100% and 100%; 100% and 89.7%; 86.7% and 75.9%, respectively). Two patients in each group underwent salvage surgery, and 2 patients in the NB group underwent chemotherapy owing to submucosal invasion. No serious complications were encountered. Recurrences were not observed

in any of the patients during the follow-up period (48-2629 days). ESD with a 1-cm safety margin may be effective for the treatment of BA and NB of the EGJ. “
“ESD of Barretts with early neoplasia has been an elusive goal because of the limitation in the complete tumor resection (R0) rate and efficiency of the procedure. ESD-U is

a PD-0332991 datasheet concept in which ESD is performed with the aim to optimize time using commercially available accessories. Circumferential incision is required, but dissection may be complete or partial and replaced by snaring whenever possible. We hypothesized that early neoplasia in Barretts could be resected with R0 resection using ESD-U. We aimed to prospectively assess the feasibility and oncological results of ESD-U in patients with Barretts early neoplasia in

the US. We enrolled consecutive patients with early neoplastic Barretts esophagus who were referred for resection after biopsies showed Barretts high-grade dysplasis Chloroambucil (HGD) or mucosal adenocarcinoma since August 2011. We used a standardized technique that includes: localization of the neoplastic area using white light, Image Enhanced Endoscopy (IEE) using the Narrow-Band Imaging (NBI) and diluted indigo carmine, circumferential incision using the Dual Knife, resection using knife or snaring, mopping (ablation of capillaries and clipping) and pathological examination using serial 2mm cuts. The primary outcome was the tumor resection rate. The secondary outcomes were complication rates and variables associated with completion of the procedure. We studied 15 consecutive lesions with mean diameter 2.4±1.6.0 cm (range 1.1 to 6.0 cm) in 10 patients (mean 60±4.8years, all men; median ASA 3 and median BMI 29). Patients were high-risk surgical candidates due to prior esophagectomy (n=3), severe co-morbid diseases (n=4), or refused surgery (n=3). Complete en-bloc R0 resection of the targeted area was achieved in all lesions, except one had positive vertical margin that required a repeat ESD to complete. 3 patients required post resection dilations, but none had bleeding or perforation. The median total procedure time was 60 minutes (mean 68±37min; range 17 to 160 min).

After 60 min of reaction at 37 °C, release of Pi was colorimetrically measured as previously described (Fiske and Subbarow, 1925). Yolk granule suspensions were obtained by gently rupturing of 24-h-old eggs in 0.4 M sucrose, 10 mM Hepes pH 7.2. Samples

Tofacitinib in vitro were washed (1 min, 10,000g, room temperature centrifugation), and fixed at room temperature for 30 min in 0.4 M sucrose, 10 mM Hepes pH 7.2, 0.5% glutaraldehyde, 0.5% formaldehyde. After washing in 0.4 M sucrose, 10 mM Hepes pH 7.2, samples were resuspended and incubated for 1 h at 37 °C in acid phosphatase reaction medium (1 mM sodium β-glycerophosphate, 2 mM CeCl3, 0.1 M sucrose, 0.1 M sodium acetate pH 4.0) ( Hulstaert et al., 1983). Controls were carried out without the substrate or in the presence of 10 mM Na+ K+ tartrate. Samples were washed twice in 0.1 M sodium acetate pH 4.0, once in 0.1 M sodium cacodylate pH 7.2 and posteriorly fixed for http://www.selleckchem.com/products/Everolimus(RAD001).html 2 h at room temperature by 2.5% glutaraldehyde, 4% formaldehyde, 0.1 M sodium cacodylate pH 7.2. Samples were then washed in cacodylate buffer, post-fixed in 1% OsO4 for 1 h at room temperature, dehydrated in ethanol series and embedded in a Polybed 812 resin. Ultrathin sections were observed in a JEOL 1200 EX transmission electron microscope, operating

at 80 kV. For X-ray microanalysis, X-rays were collected for 150 s using a Si (Li) detector with a Norvar window in a 0–10 keV energy range with a resolution of 10 eV/channel. Analysis was performed using a Noran Voyager III analyzer. Freshly-laid eggs were homogenized in 20 mM Hepes pH 7.5 and centrifuged twice for 10 min at 18,000g at 4 °C. Supernatants were centrifuged at 10,000g for 2 h at 4 °C in a Millipore Ultrafree-MC-5 centrifugal filter unit and retained samples were resuspended in 20 mM Hepes pH 7.5, and labeled “yolk protein”. Following, 40 μg of “yolk protein” was incubated

at 37 °C in a reaction medium (P8340 protease inhibitor cocktail, 2.5 mM DTT, 2.5 mM EDTA, 25 mM sodium acetate pH 4.0) containing 0.32 μg agAP protein. When specified, 10 mM Na+ K+ tartrate was used as agAP inhibitor. Following, 12.5% Histone demethylase SDS–PAGE was performed and the proteins were transferred to a nitrocellulose membrane that was blocked for 90 min with blocking buffer (0.05% TBS-Tween 20, 3% BSA). The membrane was then incubated overnight in blocking buffer containing 1:1000 PY-99 (raised against phosphotyrosine). Membrane was washed and revealed using a SuperSignal West Pico (Pierce) after incubation of 1:2000 anti-mouse peroxidase-conjugated IgG. All incubation steps were performed at room temperature. PolyP detection was performed as described (Gomes et al., 2008). Briefly, yolk granule suspensions were obtained by gently rupturing of 24-h-old eggs in 20 mM Hepes pH 7.2. Samples were washed (1 min, 10,000 g, room temperature) and incubated in 20 mM Hepes pH 7.2, 50 μg/mL DAPI for 20 min at room temperature.

Indeed, Devasthale et al. (2004) detected a decrease in brightness temperature for stronger air pollution in central Europe during the late 1980s. The cloud brightness temperature changed in low- and medium-level

and convective clouds. During episodes of strong anthropogenic emissions in Europe, the cloud-tops over and around polluted regions are higher, and their temperatures exhibited greater variability. In the area shown in Figure 1 the cloud top temperature increased during summer by 4.4 K over the land and 1.6 K over the sea. During winter the increases over the land were somewhat smaller (by 3.7 K). During the summers of the late 1980s, the brightness temperatures of low- and medium-level clouds close to emission sources changed by 2.9 K and those of convective clouds by as much as 5.2 K. This signifies the evident human impact of aerosol cloud-mediated processes in

the thermal spectral range. The impact of ship emissions on cloud INCB024360 cost properties over coastal areas was also investigated using the same Apoptosis inhibitor data set (Devasthale et al. 2006). Whereas land-based emissions were decreasing in central Europe, emissions from ships were increasing. The pollution from shipping routes in the English Channel and from the top three polluting harbours in Europe caused an increase in cloud albedo and a corresponding decrease in cloud top temperature; both parameters were more variable over coastal areas. The debate is continuing as to whether

the cloud property changes induced by ship exhaust emissions (commonly referred to as ‘ship tracks’), first observed by Conover (1966), are due to a decrease in droplet size or to an increase in the cloud liquid water path through additional droplets. Radke et al. (1989) pointed out that the latter process could well explain this finding, because the number of condensation nuclei is generally limited over the ocean, which is not the case over the land. Since large numbers of Aitken nuclei can be formed in the exhaust, ocean-going vessels could easily contribute to the anomalous formation of Aitken nuclei. Conover Adenosine (1966) specified the critical conditions for this to happen. In particular, convectively unstable situations from the surface up to a stable, low-level layer, as well as a slight supersaturation at the top of the convective layer, presumably deficient in cloud nuclei, favour the observed anomalous cloud lines. These ship tracks have been widely used together with Twomey’s theoretical work (e.g. Twomey 1977) to manifest the great importance of indirect aerosol effects in the climate system. Field experiments in marine stratocumulus clouds supported the above conclusions regarding the occurrence of indirect aerosol effects (Coakley et al. 1987). Later in 1989, Albrecht (1989), also influenced by the finding of Radke et al. (1989), formulated the basis for the so-called second indirect aerosol effect in his theoretical work.

The K-profile parameterization of Large et al. (1994) is used for vertical mixing, Selleck Roxadustat with background coefficients of 10−4 m2 s−1 for viscosity and, for our control run, 0.1×10-40.1×10-4 m2 s−1 for diffusion (κbκb). Parameter κbκb is then altered in sensitivity experiments (see Section 2.2).

Surface forcing is determined from a monthly climatology of atmospheric variables from the European Centre for Medium Range Weather Forecasts (ECMWF) Interim Reanalysis (ERA-Interim, http://apps.ecmwf.int/datasets/data/interim_full_daily) for the period of 1991–2000. These variables are used to compute surface turbulent and radiative fluxes for the ocean model by the bulk formulae of Large and Pond, 1981 and Large and Pond, 1982, according to which sea-surface heat flux and evaporation depend on sea-surface temperature. Our control experiment (CTL) is initialized with the January climatology of the GECCO reanalysis, and integrated for 40 years to reach a quasi-equilibrium state in the upper ocean. Each

of the subsequent experiments (CTL and sensitivity experiments) is then initialized with the year-40 state of CTL and integrated forward for an additional 20 years. In all the experiments, the ERA-interim and GECCO climatologies are repeatedly used for all model years. Unless stated otherwise, solutions discussed INK 128 solubility dmso in the text and shown in figures are taken from the final year of integration.

By this time, solutions are approaching equilibrium throughout the basin, particularly so near the equator. Table 1 lists the experiments we carry out. Experiment CTL is our control run in which κbκb is set everywhere to the default value κ0=0.1×10-4m2s-1. In experiment FB, κbκb is increased to κ0+Δκ=0.5×10-4m2s-1 throughout the basin. In the other experiments, κbκb is increased from κ0κ0 to κ0+Δκκ0+Δκ within specified subregions. As shown in Fig. 1, the regions are located in the eastern and western ocean, near the equator (EQE and EQW; equatorial regions), to either side of the equator (ENE, ENW, ESE, check and ESW; off-equatorial regions), and poleward of 8 °S°S or 8 °N°N (NE, NW, SE, and SW; tropical regions). Just inside the edges of each subregion, κbκb is ramped from κ0κ0 to κ0+Δκκ0+Δκ using cosine tapers of the form equation(1) r12(η)=(1±cosπη)/2,0⩽η⩽1,where ηη is a non-dimensional coordinate with a different form for each type of edge. According to (1), r1r1 decreases from 1 to 0 with ηη and vice versa for r2r2. Consider such a ramp just inside the eastern edge of a subregion and let x1x1 be the point where κbκb starts to decrease. Then, κbκb decreases from κ0+Δκκ0+Δκ to κ0κ0 across the ramp as equation(2) κb(x)=κ0+Δκr1x-x1Δx,x1⩽x⩽x1+Δx.Similarly, for the western edge of a subregion κbκb increases from κ0κ0 to κ0+Δκκ0+Δκ across the ramp as equation(3) κb(x)=κ0+Δκr2x-x2Δx,x2⩽x⩽x2+Δx.