Evidence of a universal scaling relationship for leaf CO2 drawdown along an aridity gradient

The leaf carbon isotope ratio (��13C) of C3 plants is inversely related to the drawdown of CO2 concentration during photosynthesis, which increases towards drier environments. We aimed to discriminate between the hypothesis of universal scaling, which predicts between-species responses of ��13C to aridity similar to within-species responses, and biotic homoeostasis, which predicts offsets in the ��13C of species occupying adjacent ranges. The Northeast China Transect spans 130���900 mm annual precipitation within a narrow latitude and temperature range. Leaves of 171 species were sampled at 33 sites along the transect (18 at ��� 5 sites) for dry matter, carbon (C) and nitrogen (N) content, specific leaf area (SLA) and ��13C. The ��13C of species generally followed a common relationship with the climatic moisture index (MI). Offsets between adjacent species were not observed. Trees and forbs diverged slightly at high MI. In C3 plants, ��13C predicted N per unit leaf area (Narea) better than MI. The ��13C of C4 plants was invariant with MI. SLA declined and Narea increased towards low MI in both C3 and C4 plants. The data are consistent with optimal stomatal regulation with respect to atmospheric dryness. They provide evidence for universal scaling of CO2 drawdown with aridity in C3 plants.

Problems of allometric scaling analysis: examples from mammalian reproductive biology.

Biological scaling analyses employing the widely used bivariate allometric model are beset by at least four interacting problems: (1) choice of an appropriate best-fit line with due attention to the influence of outliers; (2) objective recognition of divergent subsets in the data (allometric grades); (3) potential restrictions on statistical independence resulting from phylogenetic inertia; and (4) the need for extreme caution in inferring causation from correlation. A new non-parametric line-fitting technique has been developed that eliminates requirements for normality of distribution, greatly reduces the influence of outliers and permits objective recognition of grade shifts in substantial datasets. This technique is applied in scaling analyses of mammalian gestation periods and of neonatal body mass in primates. These analyses feed into a re-examination, conducted with partial correlation analysis, of the maternal energy hypothesis relating to mammalian brain evolution, which suggests links between body size and brain size in neonates and adults, gestation period and basal metabolic rate. Much has been made of the potential problem of phylogenetic inertia as a confounding factor in scaling analyses. However, this problem may be less severe than suspected earlier because nested analyses of variance conducted on residual variation (rather than on raw values) reveals that there is considerable variance at low taxonomic levels. In fact, limited divergence in body size between closely related species is one of the prime examples of phylogenetic inertia. One common approach to eliminating perceived problems of phylogenetic inertia in allometric analyses has been calculation of 'independent contrast values'. It is demonstrated that the reasoning behind this approach is flawed in several ways. Calculation of contrast values for closely related species of similar body size is, in fact, highly questionable, particularly when there are major deviations from the best-fit line for the scaling relationship under scrutiny.

One size fits all: stability of metabolic scaling under warming and ocean acidification in echinoderms

Responses by marine species to ocean acidification (OA) have recently been shown to be modulated by external factors including temperature, food supply and salinity. However the role of a fundamental biological parameter relevant to all organisms, that of body size, in governing responses to multiple stressors has been almost entirely overlooked. Recent consensus suggests allometric scaling of metabolism with body size differs between species, the commonly cited 'universal' mass scaling exponent (b) of �� representing an average of exponents that naturally vary. One model, the Metabolic-Level Boundaries hypothesis, provides a testable prediction: that b will decrease within species under increasing temperature. However, no previous studies have examined how metabolic scaling may be directly affected by OA. We acclimated a wide body-mass range of three common NE Atlantic echinoderms (the sea star Asterias rubens, the brittlestars Ophiothrix fragilis and Amphiura filiformis) to two levels of pCO2 and three temperatures, and metabolic rates were determined using closed-chamber respirometry. The results show that contrary to some models these echinoderm species possess a notable degree of stability in metabolic scaling under different abiotic conditions; the mass scaling exponent (b) varied in value between species, but not within species under different conditions. Additionally, we found no effect of OA on metabolic rates in any species. These data suggest responses to abiotic stressors are not modulated by body size in these species, as reflected in the stability of the metabolic scaling relationship. Such equivalence in response across ontogenetic size ranges has important implications for the stability of ecological food webs.

Regional processes in mangrove ecosystems: spatial scaling relationships, biomass, and turnover rates following catastrophic disturbance

Physiological processes and local-scale structural dynamics of mangroves are relatively well studied. Regional-scale processes, however, are not as well understood. Here we provide long-term data on trends in structure and forest turnover at a large scale, following hurricane damage in mangrove ecosystems of South Florida, U.S.A. Twelve mangrove vegetation plots were monitored at periodic intervals, between October 1992 and March 2005. Mangrove forests of this region are defined by a ���1.5 scaling relationship between mean stem diameter and stem density, mirroring self-thinning theory for mono-specific stands. This relationship is reflected in tree size frequency scaling exponents which, through time, have exhibited trends toward a community average that is indicative of full spatial resource utilization. These trends, together with an asymptotic standing biomass accumulation, indicate that coastal mangrove ecosystems do adhere to size-structured organizing principles as described for upland tree communities. Regenerative dynamics are different between areas inside and outside of the primary wind-path of Hurricane Andrew which occurred in 1992. Forest dynamic turnover rates, however, are steady through time. This suggests that ecological, more-so than structural factors, control forest productivity. In agreement, the relative mean rate of biomass growth exhibits an inverse relationship with the seasonal range of porewater salinities. The ecosystem average in forest scaling relationships may provide a useful investigative tool of mangrove community biomass relationships, as well as offer a robust indicator of general ecosystem health for use in mangrove forest ecosystem management and restoration.

Tipping the scales: Evolution of the allometric slope independent of average trait size.

The scaling of body parts is central to the expression of morphology across body sizes and to the generation of morphological diversity within and among species. Although patterns of scaling-relationship evolution have been well documented for over one hundred years, little is known regarding how selection acts to generate these patterns. In part, this is because it is unclear the extent to which the elements of log-linear scaling relationships-the intercept or mean trait size and the slope-can evolve independently. Here, using the wing-body size scaling relationship in Drosophila melanogaster as an empirical model, we use artificial selection to demonstrate that the slope of a morphological scaling relationship between an organ (the wing) and body size can evolve independently of mean organ or body size. We discuss our findings in the context of how selection likely operates on morphological scaling relationships in nature, the developmental basis for evolved changes in scaling, and the general approach of using individual-based selection experiments to study the expression and evolution of morphological scaling.

Lifespan, body size and oxygen : aerobic metabolism and oxidative stress in cultured fibroblasts /

The allometric scaling relationship observed between metabolic rate (MR) and species body mass can be partially explained by differences in cellular MR (Porter & Brand, 1995). Here, I studied cultured cell lines derived from ten mammalian species to determine whether cells propagated in an identical environment exhibited MR scaling. Oxidative and anaerobic metabolic parameters did not scale significantly with donor body mass in cultured cells, indicating the absence of an intrinsic MR setpoint. The rate of oxygen delivery has been proposed to limit cellular metabolic rates in larger organisms (West et al., 2002). As such cells were cultured under a variety of physiologically relevant oxygen tensions to investigate the effect of oxygen on cellular metabolic rates. Exposure to higher medium oxygen tensions resulted in increased metabolic rates in all cells. Higher MRs have the potential to produce more reactive oxygen species (ROS) which could cause genomic instability and thus reduced lifespan. Longer-lived species are more resistant to oxidative stress (Kapahi et al, 1999), which may be due to greater antioxidant and/or DNA repair capacities. This hypothesis was addressed by culturing primary dermal fibroblasts from eight mammalian species ranging in maximum lifespan from 5 to 120 years. Only the antioxidant manganese superoxide dismutases (MnSOD) positively scaled with species lifespan (p<0.01). Oxidative damage to DNA is primarily repaired by the base excision repair (BER) pathway. BER enzyme activities showed either no correlation or as in the case of polymerase p correlated, negatively with donor species (p<0.01 ). Typically, mammalian cells are cultured in a 20% O2 (atmospheric) environment, which is several-fold higher than cells experience in vivo. Therefore, the secondary aim of this study was to determine the effect of culturing mammalian cells at a more physiological oxygen tension (3%) on BER, and antioxidant, enzyme activities. Consistently, standard culture conditions induce higher antioxidant and DNA ba.se excision repair activities than are present under a more physiological oxygen concentration. Therefore, standard culture conditions are inappropriate for studies of oxidative stress-induced activities and species differences in fibroblast DNA BER repair capacities may represent differences in ability to respond to oxidative stress. An interesting outcome firom this study was that some inherent cellular properties are maintained in culture (i.e. stress responses) while others are not (i.e. MR).

Differences between Tethered Polyelectrolyte Chains on Bare Mica and Hydrophobically Modified Mica

This study investigates the structures of layers of amphiphilic diblock copolymers of poly(t-butyl styrene)-poly- (styrene sulfonate) (PtBS-PSS) adsorbed on both the bare mica surface (hydrophilic) and an octadecyltriethoxysilane (OTE)-modified mica surface (hydrophobic). When the surface is rendered hydrophobic, the nonsoluble block exhibits stronger interaction with the surface and higher adsorbed masses are achieved. Interaction forces between two such adsorbed layers on both substrates were measured using the surface forces apparatus. The effect of salt concentration (Cs) and molecular weight (N) on the height of the self-assembled layers (L0) was examined in each case. The resulting scaling relationship is in good agreement with predictions of the brush model, L0 ��� N1.0 in the low-salt limit and L0N-1 ��� (Cs/��)-0.32 in the salted regime, when adsorption takes place onto the hydrophobized mica surface. For adsorption on the bare mica surface, L0N-0.7 ��� Cs -0.17 agrees with the scaling prediction of the sparse tethering model. The results suggest that, on the hydrophilic bare mica surface, the adsorbed amount is not high enough to form a brush structure and only very little intermolecular stretching of the tethered chains occurs; in contrast, the presence of the hydrophobic OTE layer increases the tethering density such that the polyelectrolyte chains adopt a brush conformation.

Experimental analysis of coaxial jets: instability, flow and mixing characterization

The velocity and mixing field of two turbulent jets configurations have been experimentally characterized by means of cold- and hot-wire anemometry in order to investigate the effects of the initial conditions on the flow development. In particular, experiments have been focused on the effect of the separation wall between the two streams on the flow field. The results of the experiments have pointed out that the wake behind a thick wall separating wall has a strong influence on the flow field evolution. For instance, for nearly unitary velocity ratios, a clear vortex shedding from the wall is observable. This phenomenon enhances the mixing between the inner and outer shear layer. This enhancement in the fluctuating activity is a consequence of a local absolute instability of the flow which, for a small range of velocity ratios, behaves as an hydrodynamic oscillator with no sensibility to external perturbations. It has been suggested indeed that this absolute instability can be used as a passive method to control the flow evolution. Finally, acoustic excitation has been applied to the near field in order to verify whether or not the observed vortex shedding behind the separating wall is due to a global oscillating mode as predicted by the theory. A new scaling relationship has been also proposed to determine the preferred frequency for nearly unitary velocity ratios. The proposed law takes into account both the Reynolds number and the velocity ratio dependence of this frequency and, therefore, improves all the previously proposed relationships.

Geographical variation in shell morphology of juvenile snails (Concholepas concholepas) along the physical-chemical gradient of the Chilean coast

Changes in phenotypic traits, such as mollusc shells, are indicative of variations in selective pressure along environmental gradients. Recently, increased sea surface temperature (SST) and ocean acidification (OA) due to increased levels of carbon dioxide in the seawater have been described as selective agents that may affect the biological processes underlying shell formation in calcifying marine organisms. The benthic snail Concholepas concholepas (Muricidae) is widely distributed along the Chilean coast, and so is naturally exposed to a strong physical-chemical latitudinal gradient. In this study, based on elliptical Fourier analysis, we assess changes in shell morphology (outlines analysis) in juvenile C. concholepas collected at northern (23��S), central (33��S) and southern (39��S) locations off the Chilean coast. Shell morphology of individuals collected in northern and central regions correspond to extreme morphotypes, which is in agreement with both the observed regional differences in the shell apex outlines, the high reclassification success of individuals (discriminant function analysis) collected in these regions, and the scaling relationship in shell weight variability among regions. However, these extreme morphotypes showed similar patterns of mineralization of calcium carbonate forms (calcite and aragonite). Geographical variability in shell shape of C. concholepas described by discriminant functions was partially explained by environmental variables (pCO2, SST). This suggests the influence of corrosive waters, such as upwelling and freshwaters penetrating into the coastal ocean, upon spatial variation in shell morphology. Changes in the proportion of calcium carbonate forms precipitated by C. concholepas across their shells and its susceptibility to corrosive coastal waters are discussed.

Estimate of the total ice volume of Svalbard glaciers and their potential contribution to sea-level rise = Estimaci��n del volumen de hielo de Svalbard y su contribuci��n potencial a la subida del nivel del mar

El objetivo final de las investigaciones recogidas en esta tesis doctoral es la estimaci��n del volumen de hielo total de los ms de 1600 glaciares de Svalbard, en el ��rtico, y, con ello, su contribuci��n potencial a la subida del nivel medio del mar en un escenario de calentamiento global. Los c��lculos m��s exactos del volumen de un glaciar se efect��an a partir de medidas del espesor de hielo obtenidas con georradar. Sin embargo, estas medidas no son viables para conjuntos grandes de glaciares, debido al coste, dificultades log��sticas y tiempo requerido por ellas, especialmente en las regiones polares o de monta��a. Frente a ello, la determinaci��n de ��reas de glaciares a partir de im��genes de sat��lite s�� es viable a escalas global y regional, por lo que las relaciones de escala volumen-��rea constituyen el mecanismo m��s adecuado para las estimaciones de vol��menes globales y regionales, como las realizadas para Svalbard en esta tesis. Como parte del trabajo de tesis, hemos elaborado un inventario de los glaciares de Svalbard en los que se han efectuado radioecosondeos, y hemos realizado los c��lculos del volumen de hielo de m��s de 80 cuencas glaciares de Svalbard a partir de datos de georradar. Estos vol��menes han sido utilizados para calibrar las relaciones volumen-��rea desarrolladas en la tesis. Los datos de georradar han sido obtenidos en diversas campa��as llevadas a cabo por grupos de investigaci��n internacionales, gran parte de ellas lideradas por el Grupo de Simulaci��n Num��rica en Ciencias e Ingenier��a de la Universidad Polit��cnica de Madrid, del que forman parte la doctoranda y los directores de tesis. Adem��s, se ha desarrollado una metodolog��a para la estimaci��n del error en el c��lculo de volumen, que aporta una novedosa t��cnica de c��lculo del error de interpolaci��n para conjuntos de datos del tipo de los obtenidos con perfiles de georradar, que presentan distribuciones espaciales con unos patrones muy caracter��sticos pero con una densidad de datos muy irregular. Hemos obtenido en este trabajo de tesis relaciones de escala espec��ficas para los glaciares de Svalbard, explorando la sensibilidad de los par��metros a diferentes morfolog��as glaciares, e incorporando nuevas variables. En particular, hemos efectuado experimentos orientados a verificar si las relaciones de escala obtenidas caracterizando los glaciares individuales por su tama��o, pendiente o forma implican diferencias significativas en el volumen total estimado para los glaciares de Svalbard, y si esta partici��n implica alg��n patr��n significativo en los par��metros de las relaciones de escala. Nuestros resultados indican que, para un valor constante del factor multiplicativo de la relacin de escala, el exponente que afecta al ��rea en la relaci��n volumen-��rea decrece seg��n aumentan la pendiente y el factor de forma, mientras que las clasificaciones basadas en tama��o no muestran un patr��n significativo. Esto significa que los glaciares con mayores pendientes y de tipo circo son menos sensibles a los cambios de ��rea. Adem��s, los vol��menes de la poblaci��n total de los glaciares de Svalbard calculados con fraccionamiento en grupos por tama��o y pendiente son un 1-4% menores que los obtenidas usando la totalidad de glaciares sin fraccionamiento en grupos, mientras que los vol��menes calculados fraccionando por forma son un 3-5% mayores. Tambi��n realizamos experimentos multivariable para obtener estimaciones ��ptimas del volumen total mediante una combinaci��n de distintos predictores. Nuestros resultados muestran que un modelo potencial simple volumen-��rea explica el 98.6% de la varianza. S��lo el predictor longitud del glaciar proporciona significaci��n estad��stica cuando se usa adem��s del ��rea del glaciar, aunque el coeficiente de determinaci��n disminuye en comparaci��n con el modelo m��s simple V-A. El predictor intervalo de altitud no proporciona informaci��n adicional cuando se usa adem��s del ��rea del glaciar. Nuestras estimaciones del volumen de la totalidad de glaciares de Svalbard usando las diferentes relaciones de escala obtenidas en esta tesis oscilan entre 6890 y 8106 km3, con errores relativos del orden de 6.6-8.1%. El valor medio de nuestras estimaciones, que puede ser considerado como nuestra mejor estimaci��n del volumen, es de 7.504 km3. En t��rminos de equivalente en nivel del mar (SLE), nuestras estimaciones corresponden a una subida potencial del nivel del mar de 17-20 mm SLE, promediando 19_2 mm SLE, donde el error corresponde al error en volumen antes indicado. En comparaci��n, las estimaciones usando las relaciones V-A de otros autores son de 13-26 mm SLE, promediando 20 _ 2 mm SLE, donde el error representa la desviaci��n est��ndar de las distintas estimaciones. ABSTRACT The final aim of the research involved in this doctoral thesis is the estimation of the total ice volume of the more than 1600 glaciers of Svalbard, in the Arctic region, and thus their potential contribution to sea-level rise under a global warming scenario. The most accurate calculations of glacier volumes are those based on ice-thicknesses measured by groundpenetrating radar (GPR). However, such measurements are not viable for very large sets of glaciers, due to their cost, logistic difficulties and time requirements, especially in polar or mountain regions. On the contrary, the calculation of glacier areas from satellite images is perfectly viable at global and regional scales, so the volume-area scaling relationships are the most useful tool to determine glacier volumes at global and regional scales, as done for Svalbard in this PhD thesis. As part of the PhD work, we have compiled an inventory of the radio-echo sounded glaciers in Svalbard, and we have performed the volume calculations for more than 80 glacier basins in Svalbard from GPR data. These volumes have been used to calibrate the volume-area relationships derived in this dissertation. Such GPR data have been obtained during fieldwork campaigns carried out by international teams, often lead by the Group of Numerical Simulation in Science and Engineering of the Technical University of Madrid, to which the PhD candidate and her supervisors belong. Furthermore, we have developed a methodology to estimate the error in the volume calculation, which includes a novel technique to calculate the interpolation error for data sets of the type produced by GPR profiling, which show very characteristic data distribution patterns but with very irregular data density. We have derived in this dissertation scaling relationships specific for Svalbard glaciers, exploring the sensitivity of the scaling parameters to different glacier morphologies and adding new variables. In particular, we did experiments aimed to verify whether scaling relationships obtained through characterization of individual glacier shape, slope and size imply significant differences in the estimated volume of the total population of Svalbard glaciers, and whether this partitioning implies any noticeable pattern in the scaling relationship parameters. Our results indicate that, for a fixed value of the factor in the scaling relationship, the exponent of the area in the volume-area relationship decreases as slope and shape increase, whereas size-based classifications do not reveal any clear trend. This means that steep slopes and cirque-type glaciers are less sensitive to changes in glacier area. Moreover, the volumes of the total population of Svalbard glaciers calculated according to partitioning in subgroups by size and slope are smaller (by 1-4%) than that obtained considering all glaciers without partitioning into subgroups, whereas the volumes calculated according to partitioning in subgroups by shape are 3-5% larger. We also did multivariate experiments attempting to optimally predict the volume of Svalbard glaciers from a combination of different predictors. Our results show that a simple power-type V-A model explains 98.6% of the variance. Only the predictor glacier length provides statistical significance when used in addition to the predictor glacier area, though the coefficient of determination decreases as compared with the simpler V-A model. The predictor elevation range did not provide any additional information when used in addition to glacier area. Our estimates of the volume of the entire population of Svalbard glaciers using the different scaling relationships that we have derived along this thesis range within 6890-8106 km3, with estimated relative errors in total volume of the order of 6.6-8.1% The average value of all of our estimates, which could be used as a best estimate for the volume, is 7,504 km3. In terms of sea-level equivalent (SLE), our volume estimates correspond to a potential contribution to sea-level rise within 17-20 mm SLE, averaging 19 _ 2 mm SLE, where the quoted error corresponds to our estimated relative error in volume. For comparison, the estimates using the V-A scaling relations found in the literature range within 13-26 mm SLE, averaging 20 _ 2 mm SLE, where the quoted error represents the standard deviation of the different estimates.

Immunological synapse: a mathematical model of the bond formation process:mathematical modelling of the immature synapse

The cell:cell bond between an immune cell and an antigen presenting cell is a necessary event in the activation of the adaptive immune response. At the juncture between the cells, cell surface molecules on the opposing cells form non-covalent bonds and a distinct patterning is observed that is termed the immunological synapse. An important binding molecule in the synapse is the T-cell receptor (TCR), that is responsible for antigen recognition through its binding with a major-histocompatibility complex with bound peptide (pMHC). This bond leads to intracellular signalling events that culminate in the activation of the T-cell, and ultimately leads to the expression of the immune eector function. The temporal analysis of the TCR bonds during the formation of the immunological synapse presents a problem to biologists, due to the spatio-temporal scales (nanometers and picoseconds) that compare with experimental uncertainty limits. In this study, a linear stochastic model, derived from a nonlinear model of the synapse, is used to analyse the temporal dynamics of the bond attachments for the TCR. Mathematical analysis and numerical methods are employed to analyse the qualitative dynamics of the nonequilibrium membrane dynamics, with the specic aim of calculating the average persistence time for the TCR:pMHC bond. A single-threshold method, that has been previously used to successfully calculate the TCR:pMHC contact path sizes in the synapse, is applied to produce results for the average contact times of the TCR:pMHC bonds. This method is extended through the development of a two-threshold method, that produces results suggesting the average time persistence for the TCR:pMHC bond is in the order of 2-4 seconds, values that agree with experimental evidence for TCR signalling. The study reveals two distinct scaling regimes in the time persistent survival probability density prole of these bonds, one dominated by thermal uctuations and the other associated with the TCR signalling. Analysis of the thermal fluctuation regime reveals a minimal contribution to the average time persistence calculation, that has an important biological implication when comparing the probabilistic models to experimental evidence. In cases where only a few statistics can be gathered from experimental conditions, the results are unlikely to match the probabilistic predictions. The results also identify a rescaling relationship between the thermal noise and the bond length, suggesting a recalibration of the experimental conditions, to adhere to this scaling relationship, will enable biologists to identify the start of the signalling regime for previously unobserved receptor:ligand bonds. Also, the regime associated with TCR signalling exhibits a universal decay rate for the persistence probability, that is independent of the bond length.

A note on the dual scaling of dominance data and its relationship to correspondence analysis

Dual scaling of a subjects-by-objects table of dominance data (preferences,paired comparisons and successive categories data) has been contrasted with correspondence analysis, as if the two techniques were somehow different. In this note we show that dual scaling of dominance data is equivalent to the correspondence analysis of a table which is doubled with respect to subjects. We also show that the results of both methods can be recovered from a principal components analysis of the undoubled dominance table which is centred with respect to subject means.

Hipsometric relationship modeling using data sampled in tree scaling and inventory plots

This work evaluated eight hypsometric models to represent tree height-diameter relationship, using data obtained from the scaling of 118 trees and 25 inventory plots. Residue graphic analysis and percent deviation mean criteria, qui-square test precision, residual standard error between real and estimated heights and the graybill f test were adopted. The identity of the hypsometric models was also verified by applying the F(Ho) test on the plot data grouped to the scaling data. It was concluded that better accuracy can be obtained by using the model prodan, with h and d1,3 data measured in 10 trees by plots grouped into these scaling data measurements of even-aged forest stands.

A note on a practical relationship between filter coefficients and scaling and wavelet functions of Discrete Wavelet Transforms

In this paper, the relationship between the filter coefficients and the scaling and wavelet functions of the Discrete Wavelet Transform is presented and exemplified from a practical point-of-view. The explanations complement the wavelet theory, that is well documented in the literature, being important for researchers who work with this tool for time-frequency analysis. (c) 2011 Elsevier Ltd. All rights reserved.

Analysis of UV spectral bands using multidimensional scaling

This study describes the change of the ultraviolet spectral bands starting from 0.1 to 5.0 nm slit width in the spectral range of 200���400 nm. The analysis of the spectral bands is carried out by using the multidimensional scaling (MDS) approach to reach the latent spectral background. This approach indicates that 0.1 nm slit width gives higher-order noise together with better spectral details. Thus, 5.0 nm slit width possesses the higher peak amplitude and lower-order noise together with poor spectral details. In the above-mentioned conditions, the main problem is to find the relationship between the spectral band properties and the slit width. For this aim, the MDS tool is to used recognize the hidden information of the ultraviolet spectra of sildenafil citrate by using a ShimadzuUV���VIS 2550, which is in theworld the best double monochromator instrument. In this study, the proposed mathematical approach gives the rich findings for the efficient use of the spectrophotometer in the qualitative and quantitative studies.