The Coupled Aerosol and Tracer Transport model to the Brazilian developments on the Regional Atmospheric Modeling System (CATT-BRAMS) - Part 1: Model description and evaluation

We introduce the Coupled Aerosol and Tracer Transport model to the Brazilian developments on the Regional Atmospheric Modeling System (CATT-BRAMS). CATT-BRAMS is an on-line transport model fully consistent with the simulated atmospheric dynamics. Emission sources from biomass burning and urban-industrial-vehicular activities for trace gases and from biomass burning aerosol particles are obtained from several published datasets and remote sensing information. The tracer and aerosol mass concentration prognostics include the effects of sub-grid scale turbulence in the planetary boundary layer, convective transport by shallow and deep moist convection, wet and dry deposition, and plume rise associated with vegetation fires in addition to the grid scale transport. The radiation parameterization takes into account the interaction between the simulated biomass burning aerosol particles and short and long wave radiation. The atmospheric model BRAMS is based on the Regional Atmospheric Modeling System (RAMS), with several improvements associated with cumulus convection representation, soil moisture initialization and surface scheme tuned for the tropics, among others. In this paper the CATT-BRAMS model is used to simulate carbon monoxide and particulate material (PM(2.5)) surface fluxes and atmospheric transport during the 2002 LBA field campaigns, conducted during the transition from the dry to wet season in the southwest Amazon Basin. Model evaluation is addressed with comparisons between model results and near surface, radiosondes and airborne measurements performed during the field campaign, as well as remote sensing derived products. We show the matching of emissions strengths to observed carbon monoxide in the LBA campaign. A relatively good comparison to the MOPITT data, in spite of the fact that MOPITT a priori assumptions imply several difficulties, is also obtained.

Turbulent magnetic pumping in a Babcock-Leighton solar dynamo model

Context. The turbulent pumping effect corresponds to the transport of magnetic flux due to the presence of density and turbulence gradients in convectively unstable layers. In the induction equation it appears as an advective term and for this reason it is expected to be important in the solar and stellar dynamo processes. Aims. We explore the effects of turbulent pumping in a flux-dominated Babcock-Leighton solar dynamo model with a solar-like rotation law. Methods. As a first step, only vertical pumping has been considered through the inclusion of a radial diamagnetic term in the induction equation. In the second step, a latitudinal pumping term was included and then, a near-surface shear was included. Results. The results reveal the importance of the pumping mechanism in solving current limitations in mean field dynamo modeling, such as the storage of the magnetic flux and the latitudinal distribution of the sunspots. If a meridional flow is assumed to be present only in the upper part of the convective zone, it is the full turbulent pumping that regulates both the period of the solar cycle and the latitudinal distribution of the sunspot activity. In models that consider shear near the surface, a second shell of toroidal field is generated above r = 0.95 R(circle dot) at all latitudes. If the full pumping is also included, the polar toroidal fields are efficiently advected inwards, and the toroidal magnetic activity survives only at the observed latitudes near the equator. With regard to the parity of the magnetic field, only models that combine turbulent pumping with near-surface shear always converge to the dipolar parity. Conclusions. This result suggests that, under the Babcock-Leighton approach, the equartorward motion of the observed magnetic activity is governed by the latitudinal pumping of the toroidal magnetic field rather than by a large scale coherent meridional flow. Our results support the idea that the parity problem is related to the quadrupolar imprint of the meridional flow on the poloidal component of the magnetic field and the turbulent pumping positively contributes to wash out this imprint.

uvby-beta photometry of solar twins The solar colors, model atmospheres, and the T(eff) and metallicity scales

Aims. Solar colors have been determined on the uvby-beta photometric system to test absolute solar fluxes, to examine colors predicted by model atmospheres as a function of stellar parameters (T(eff), log g, [Fe/H]), and to probe zero-points of T(eff) and metallicity scales. Methods. New uvby-beta photometry is presented for 73 solar-twin candidates. Most stars of our sample have also been observed spectroscopically to obtain accurate stellar parameters. Using the stars that most closely resemble the Sun, and complementing our data with photometry available in the literature, the solar colors on the uvby-beta system have been inferred. Our solar colors are compared with synthetic solar colors computed from absolute solar spectra and from the latest Kurucz (ATLAS9) and MARCS model atmospheres. The zero-points of different T(eff) and metallicity scales are verified and corrections are proposed. Results. Our solar colors are (b - y)(circle dot) = 0.4105 +/- 0.0015, m(1,circle dot) = 0.2122 +/- 0.0018, c(1,circle dot) = 0.3319 +/- 0.0054, and beta(circle dot) = 2.5915 +/- 0.0024. The (b - y)(circle dot) and m(1,circle dot) colors obtained from absolute spectrophotometry of the Sun agree within 3-sigma with the solar colors derived here when the photometric zero-points are determined from either the STIS HST observations of Vega or an ATLAS9 Vega model, but the c(1,circle dot) and beta(circle dot) synthetic colors inferred from absolute solar spectra agree with our solar colors only when the zero-points based on the ATLAS9 model are adopted. The Kurucz solar model provides a better fit to our observations than the MARCS model. For photometric values computed from the Kurucz models, (b - y)(circle dot) and m(1,circle dot) are in excellent agreement with our solar colors independently of the adopted zero-points, but for c(1,circle dot) and beta circle dot agreement is found only when adopting the ATLAS9 zero-points. The c(1,circle dot) color computed from both the Kurucz and MARCS models is the most discrepant, probably revealing problems either with the models or observations in the u band. The T(eff) calibration of Alonso and collaborators has the poorest performance (similar to 140 K off), while the relation of Casagrande and collaborators is the most accurate (within 10 K). We confirm that the Ramirez & Melendez uvby metallicity calibration, recommended by Arnadottir and collaborators to obtain [Fe/H] in F, G, and K dwarfs, needs a small (similar to 10%) zero-point correction to place the stars and the Sun on the same metallicity scale. Finally, we confirm that the c(1) index in solar analogs has a strong metallicity sensitivity.

Cyclic variability of the circumstellar disk of the Be star zeta Tauri II. Testing the 2D global disk oscillation model

Context. About 2/3 of the Be stars present the so-called V/R variations, a phenomenon characterized by the quasi-cyclic variation in the ratio between the violet and red emission peaks of the HI emission lines. These variations are generally explained by global oscillations in the circumstellar disk forming a one-armed spiral density pattern that precesses around the star with a period of a few years. Aims. This paper presents self-consistent models of polarimetric, photometric, spectrophotometric, and interferometric observations of the classical Be star zeta Tauri. The primary goal is to conduct a critical quantitative test of the global oscillation scenario. Methods. Detailed three-dimensional, NLTE radiative transfer calculations were carried out using the radiative transfer code HDUST. The most up-to-date research on Be stars was used as input for the code in order to include a physically realistic description for the central star and the circumstellar disk. The model adopts a rotationally deformed, gravity darkened central star, surrounded by a disk whose unperturbed state is given by a steady-state viscous decretion disk model. It is further assumed that this disk is in vertical hydrostatic equilibrium. Results. By adopting a viscous decretion disk model for zeta Tauri and a rigorous solution of the radiative transfer, a very good fit of the time-average properties of the disk was obtained. This provides strong theoretical evidence that the viscous decretion disk model is the mechanism responsible for disk formation. The global oscillation model successfully fitted spatially resolved VLTI/AMBER observations and the temporal V/R variations in the H alpha and Br gamma lines. This result convincingly demonstrates that the oscillation pattern in the disk is a one-armed spiral. Possible model shortcomings, as well as suggestions for future improvements, are also discussed.

Human Dental Pulp Cells: A New Source of Cell Therapy in a Mouse Model of Compressive Spinal Cord Injury

Strategies aimed at improving spinal cord regeneration after trauma are still challenging neurologists and neuroscientists throughout the world. Many cell-based therapies have been tested, with limited success in terms of functional outcome. In this study, we investigated the effects of human dental pulp cells (HDPCs) in a mouse model of compressive spinal cord injury (SCI). These cells present some advantages, such as the ease of the extraction process, and expression of trophic factors and embryonic markers from both ecto-mesenchymal and mesenchymal components. Young adult female C57/BL6 mice were subjected to laminectomy at T9 and compression of the spinal cord with a vascular clip for 1 min. The cells were transplanted 7 days or 28 days after the lesion, in order to compare the recovery when treatment is applied in a subacute or chronic phase. We performed quantitative analyses of white-matter preservation, trophic-factor expression and quantification, and ultrastructural and functional analysis. Our results for the HDPC-transplanted animals showed better white-matter preservation than the DMEM groups, higher levels of trophic-factor expression in the tissue, better tissue organization, and the presence of many axons being myelinated by either Schwann cells or oligodendrocytes, in addition to the presence of some healthy-appearing intact neurons with synapse contacts on their cell bodies. We also demonstrated that HDPCs were able to express some glial markers such as GFAP and S-100. The functional analysis also showed locomotor improvement in these animals. Based on these findings, we propose that HDPCs may be feasible candidates for therapeutic intervention after SCI and central nervous system disorders in humans.

Renal denervation in an animal model of diabetes and hypertension: Impact on the autonomic nervous system and nephropathy

Background: The effects of renal denervation on cardiovascular reflexes and markers of nephropathy in diabetic-hypertensive rats have not yet been explored. Methods: Aim: To evaluate the effects of renal denervation on nephropathy development mechanisms (blood pressure, cardiovascular autonomic changes, renal GLUT2) in diabetic-hypertensive rats. Forty-one male spontaneously hypertensive rats (SHR) similar to 250 g were injected with STZ or not; 30 days later, surgical renal denervation (RD) or sham procedure was performed; 15 days later, glycemia and albuminuria (ELISA) were evaluated. Catheters were implanted into the femoral artery to evaluate arterial pressure (AP) and heart rate variability (spectral analysis) one day later in conscious animals. Animals were killed, kidneys removed, and cortical renal GLUT2 quantified (Western blotting). Results: Higher glycemia (p < 0.05) and lower mean AP were observed in diabetics vs. nondiabetics (p < 0.05). Heart rate was higher in renal-denervated hypertensive and lower in diabetic-hypertensive rats (384.8 +/- 37, 431.3 +/- 36, 316.2 +/- 5, 363.8 +/- 12 bpm in SHR, RD-SHR, STZ-SHR and RD-STZ-SHR, respectively). Heart rate variability was higher in renal-denervated diabetic-hypertensive rats (55.75 +/- 25.21, 73.40 +/- 53.30, 148.4 +/- 93 in RD-SHR, STZ-SHR-and RD-STZ-SHR, respectively, p < 0.05), as well as the LF component of AP variability (1.62 +/- 0.9, 2.12 +/- 0.9, 7.38 +/- 6.5 in RD-SHR, STZ-SHR and RD-STZ-SHR, respectively, p < 0.05). GLUT2 renal content was higher in all groups vs. SHR. Conclusions: Renal denervation in diabetic-hypertensive rats improved previously reduced heart rate variability. The GLUT2 equally overexpressed by diabetes and renal denervation may represent a maximal derangement effect of each condition.

Melatonin treatment decreases c-fos expression in a headache model induced by capsaicin

The aim of the present work was to analyze c-fos response within the trigeminal nucleus caudalis (TNC) of pinealectomized rats and animals that received intraperitoneal melatonin, after intracisternal infusion of capsaicin, used to induce intracranial trigeminovascular stimulation. Experimental groups consisted of animals that received vehicle solution (saline-ethanol-Tween 80, 8:1:1, diluted 1:50) only (VEI, n = 5); animals that received capsaicin solution (200 nM) only (CAP, n = 6); animals submitted to pinealectomy (PX, n = 5); sham-operated animals (SH, n = 5); animals submitted to pinealectomy followed by capsaicin stimulation (200 nM) after 15 days (PX + CAP, n = 7); and animals that received capsaicin solution (200 nM) and intraperitoneal melatonin (10 mg/kg) (CAP + MEL, n = 5). Control rats, receiving vehicle in the cisterna magna, showed a small number of c-fos-positive cells in the TNC (layer I/II) as well as the sham-operated and pinealectomized rats, when compared to animals stimulated by capsaicin. On the other hand, pinealectomized rats, which received capsaicin, presented the highest number of c-fos-positive cells. Animals receiving capsaicin and melatonin treatment had similar expression of the vehicle group. Our data provide experimental evidence to support the role of melatonin and pineal gland in the pathophysiology of neurovascular headaches.

Collagen Hydrolysate Intake Increases Skin Collagen Expression and Suppresses Matrix Metalloproteinase 2 Activity

The effect of daily ingestion of collagen hydrolysate (CH) on skin extracellular matrix proteins was investigated. Four-week-old male Wistar rats were fed a modified AIN-93 diet containing 12% casein as the reference group or CH as the treatment group. A control group was established in which animals were fed a non-protein-modified AIN-93 diet. The diets were administered continuously for 4 weeks when six fresh skin samples from each group were assembled and subjected to extraction of protein. Type I and IV collagens were studied by immunoblot, and activities of matrix metalloproteinase (MMP) 2 and 9 were assessed by zymography. The relative amount of type I and IV collagens was significantly (P<.05) increased after CH intake compared with the reference diet group (casein). Moreover, CH uptake significantly decreased both proenzyme and active forms of MMP2 compared with casein and control groups (P<.05). In contrast, CH ingestion did not influence on MMP9 activity. These results suggest that CH may reduce aging-related changes of the extracellular matrix by stimulating anabolic processes in skin tissue.

Mechanisms of Vascular Damage by Hemorrhagic Snake Venom Metalloproteinases: Tissue Distribution and In Situ Hydrolysis

Background: Envenoming by viper snakes constitutes an important public health problem in Brazil and other developing countries. Local hemorrhage is an important symptom of these accidents and is correlated with the action of snake venom metalloproteinases (SVMPs). The degradation of vascular basement membrane has been proposed as a key event for the capillary vessel disruption. However, SVMPs that present similar catalytic activity towards extracellular matrix proteins differ in their hemorrhagic activity, suggesting that other mechanisms might be contributing to the accumulation of SVMPs at the snakebite area allowing capillary disruption. Methodology/Principal Findings: In this work, we compared the tissue distribution and degradation of extracellular matrix proteins induced by jararhagin (highly hemorrhagic SVMP) and BnP1 (weakly hemorrhagic SVMP) using the mouse skin as experimental model. Jararhagin induced strong hemorrhage accompanied by hydrolysis of collagen fibers in the hypodermis and a marked degradation of type IV collagen at the vascular basement membrane. In contrast, BnP1 induced only a mild hemorrhage and did not disrupt collagen fibers or type IV collagen. Injection of Alexa488-labeled jararhagin revealed fluorescent staining around capillary vessels and co-localization with basement membrane type IV collagen. The same distribution pattern was detected with jararhagin-C (disintegrin-like/cysteine-rich domains of jararhagin). In opposition, BnP1 did not accumulate in the tissues. Conclusions/Significance: These results show a particular tissue distribution of hemorrhagic toxins accumulating at the basement membrane. This probably occurs through binding to collagens, which are drastically hydrolyzed at the sites of hemorrhagic lesions. Toxin accumulation near blood vessels explains enhanced catalysis of basement membrane components, resulting in the strong hemorrhagic activity of SVMPs. This is a novel mechanism that underlies the difference between hemorrhagic and non-hemorrhagic SVMPs, improving the understanding of snakebite pathology.

The Thermal Effects of Therapeutic Lasers with 810 and 904 nm Wavelengths on Human Skin

Objective: To investigate the effect of therapeutic infrared class 3B laser irradiation on skin temperature in healthy participants of differing skin color, age, and gender. Background: Little is known about the potential thermal effects of Low Level Laser Therapy (LLLT) irradiation on human skin. Methods: Skin temperature was measured in 40 healthy volunteers with a thermographic camera at laser irradiated and control (non-irradiated) areas on the skin. Six irradiation doses (2-12 J) were delivered from a 200mW, 810nm laser and a 60mW, 904nm laser, respectively. Results: Thermal effects of therapeutic LLLT using doses recommended in the World Association for Laser Therapy (WALT) guidelines were insignificant; below 1.5 degrees C in light, medium, and dark skin. When higher irradiation doses were used, the 60mW, 904 nm laser produced significantly (p < 0.01) higher temperatures in dark skin (5.7, SD +/- 1.8 degrees C at 12 J) than in light skin, although no participants requested termination of LLLT. However, irradiation with a 200mW, 810nm laser induced three to six times more heat in dark skin than in the other skin color groups. Eight of 13 participants with dark skin asked for LLLT to be stopped because of uncomfortable heating. The maximal increase in skin temperature was 22.3 degrees C. Conclusions: The thermal effects of LLLT at doses recommended by WALT-guidelines for musculoskeletal and inflammatory conditions are negligible (< 1.5 degrees C) in light, medium, and dark skin. However, higher LLLT doses delivered with a strong 3B laser (200mW) are capable of increasing skin temperature significantly and these photothermal effects may exceed the thermal pain threshold for humans with dark skin color.

Induction of Heme Oxygenase-1 Can Halt and Even Reverse Renal Tubule-Interstitial Fibrosis

Background: The tubule-interstitial fibrosis is the hallmark of progressive renal disease and is strongly associated with inflammation of this compartment. Heme-oxygenase-1 (HO-1) is a cytoprotective molecule that has been shown to be beneficial in various models of renal injury. However, the role of HO-1 in reversing an established renal scar has not yet been addressed. Aim: We explored the ability of HO-1 to halt and reverse the establishment of fibrosis in an experimental model of chronic renal disease. Methods: Sprague-Dawley male rats were subjected to unilateral ureteral obstruction (UUO) and divided into two groups: non-treated and Hemin-treated. To study the prevention of fibrosis, animals were pre-treated with Hemin at days -2 and -1 prior to UUO. To investigate whether HO-1 could reverse established fibrosis, Hemin therapy was given at days 6 and 7 post-surgery. After 7 and/or 14 days, animals were sacrificed and blood, urine and kidney tissue samples were collected for analyses. Renal function was determined by assessing the serum creatinine, inulin clearance, proteinuria/creatininuria ratio and extent of albuminuria. Arterial blood pressure was measured and fibrosis was quantified by Picrosirius staining. Gene and protein expression of pro-inflammatory and pro-fibrotic molecules, as well as HO-1 were performed. Results: Pre-treatment with Hemin upregulated HO-1 expression and significantly reduced proteinuria, albuminuria, inflammation and pro-fibrotic protein and gene expressions in animals subjected to UUO. Interestingly, the delayed treatment with Hemin was also able to reduce renal dysfunction and to decrease the expression of pro-inflammatory molecules, all in association with significantly reduced levels of fibrosis-related molecules and collagen deposition. Finally, TGF-beta protein production was significantly lower in Hemin-treated animals. Conclusion: Treatment with Hemin was able both to prevent the progression of fibrosis and to reverse an established renal scar. Modulation of inflammation appears to be the major mechanism behind HO-1 cytoprotection.

Respiratory allergy to Blomia tropicalis: Immune response in four syngeneic mouse strains and assessment of a low allergen-dose, short-term experimental model

Background: The dust mite Blomia tropicalis is an important source of aeroallergens in tropical areas. Although a mouse model for B. tropicalis extract (BtE)-induced asthma has been described, no study comparing different mouse strains in this asthma model has been reported. The relevance and reproducibility of experimental animal models of allergy depends on the genetic background of the animal, the molecular composition of the allergen and the experimental protocol. Objectives: This work had two objectives. The first was to study the anti-B. tropicalis allergic responses in different mouse strains using a short-term model of respiratory allergy to BtE. This study included the comparison of the allergic responses elicited by BtE with those elicited by ovalbumin in mice of the strain that responded better to BtE sensitization. The second objective was to investigate whether the best responder mouse strain could be used in an experimental model of allergy employing relatively low BtE doses. Methods: Groups of mice of four different syngeneic strains were sensitized subcutaneously with 100 mu g of BtE on days 0 and 7 and challenged four times intranasally, at days 8, 10, 12, and 14, with 10 mu g of BtE. A/J mice, that were the best responders to BtE sensitization, were used to compare the B. tropicalis-specific asthma experimental model with the conventional experimental model of ovalbumin (OVA)-specific asthma. A/J mice were also sensitized with a lower dose of BtE. Results: Mice of all strains had lung inflammatory-cell infiltration and increased levels of anti-BtE IgE antibodies, but these responses were significantly more intense in A/J mice than in CBA/J, BALB/c or C57BL/6J mice. Immunization of A/J mice with BtE induced a more intense airway eosinophil influx, higher levels of total IgE, similar airway hyperreactivity to methacholine but less intense mucous production, and lower levels of specific IgE, IgG1 and IgG2 antibodies than sensitization with OVA. Finally, immunization with a relatively low BtE dose (10 mu g per subcutaneous injection per mouse) was able to sensitize A/J mice, which were the best responders to high-dose BtE immunization, for the development of allergy-associated immune and lung inflammatory responses. Conclusions: The described short-term model of BtE-induced allergic lung disease is reproducible in different syngeneic mouse strains, and mice of the A/J strain was the most responsive to it. In addition, it was shown that OVA and BtE induce quantitatively different immune responses in A/J mice and that the experimental model can be set up with low amounts of BtE.

Tamoxifen Is Effective in the Treatment of Leishmania amazonensis Infections in Mice

Background: Chemotherapy is still a critical issue in the management of leishmaniasis. Until recently, pentavalent antimonials, amphotericin B or pentamidine compounded the classical arsenal of treatment. All these drugs are toxic and have to be administered by the parenteral route. Tamoxifen has been used as an antiestrogen in the treatment and prevention of breast cancer for many years. Its safety and pharmacological profiles are well established in humans. We have shown that tamoxifen is active as an antileishmanial compound in vitro, and in this paper we analyzed the efficacy of tamoxifen for the treatment of mice infected with Leishmania amazonensis, an etiological agent of localized cutaneous leishmaniasis and the main cause of diffuse cutaneous leishmaniasis in South America. Methodology/Principal Findings: BALB/c mice were infected with L. amazonensis promastigotes. Five weeks post-infection, treatment with 15 daily intraperitoneal injections of 20 mg/kg tamoxifen was administered. Lesion and ulcer sizes were recorded and parasite burden quantified by limiting dilution. A significant decrease in lesion size and ulcer development was noted in mice treated with tamoxifen as compared to control untreated animals. Parasite burden in the inoculation site at the end of treatment was reduced from 10(8.5 +/- 0.7) in control untreated animals to 10(5.0 +/- 0.0) in tamoxifen-treated mice. Parasite load was also reduced in the draining lymph nodes. The reduction in parasite number was sustained: 6 weeks after the end of treatment, 10(15.5 +/- 0.5) parasites were quantified from untreated animals, as opposed to 10(5.1 +/- 0.1) parasites detected in treated mice. Conclusions/Significance: Treatment of BALB/c mice infected with L. amazonensis for 15 days with tamoxifen resulted in significant decrease in lesion size and parasite burden. BALB/c mice infected with L. amazonensis represents a model of extreme susceptibility, and the striking and sustained reduction in the number of parasites in treated animals supports the proposal of further testing of this drug in other models of leishmaniasis.

The Coupled Aerosol and Tracer Transport model to the Brazilian developments on the Regional Atmospheric Modeling System (CATT-BRAMS) - Part 2: Model sensitivity to the biomass burning

We describe an estimation technique for biomass burning emissions in South America based on a combination of remote-sensing fire products and field observations, the Brazilian Biomass Burning Emission Model (3BEM). For each fire pixel detected by remote sensing, the mass of the emitted tracer is calculated based on field observations of fire properties related to the type of vegetation burning. The burnt area is estimated from the instantaneous fire size retrieved by remote sensing, when available, or from statistical properties of the burn scars. The sources are then spatially and temporally distributed and assimilated daily by the Coupled Aerosol and Tracer Transport model to the Brazilian developments on the Regional Atmospheric Modeling System (CATT-BRAMS) in order to perform the prognosis of related tracer concentrations. Three other biomass burning inventories, including GFEDv2 and EDGAR, are simultaneously used to compare the emission strength in terms of the resultant tracer distribution. We also assess the effect of using the daily time resolution of fire emissions by including runs with monthly-averaged emissions. We evaluate the performance of the model using the different emission estimation techniques by comparing the model results with direct measurements of carbon monoxide both near-surface and airborne, as well as remote sensing derived products. The model results obtained using the 3BEM methodology of estimation introduced in this paper show relatively good agreement with the direct measurements and MOPITT data product, suggesting the reliability of the model at local to regional scales.

Model Independent Tests of Skyrmions and Their Holographic Cousins

We describe a new exact relation for large N(c) QCD for the long-distance behavior of baryon form factors in the chiral limit. This model-independent relation is used to test the consistency of the structure of several baryon models. All 4D semiclassical chiral soliton models satisfy the relation, as does the Pomarol-Wulzer holographic model of baryons as 5D Skyrmions. However, remarkably, we find that the holographic model treating baryons as instantons in the Sakai-Sugimoto model does not satisfy the relation.