Uction of hierarchical unit definitions. The exponent, scale and multiplier attributes
Uction of hierarchical unit definitions. The exponent, scale and multiplier attributes: The optional exponent attribute on Unit represents an exponent on the unit. Its default value is ” ” (a single). A Unit object also has an optional scale attribute; its value has to be an integer exponent to get a poweroften multiplier utilised to set the scale with the unit. By way of example, a unit obtaining a kind value of ” gram” plus a scale worth of ” 3″ signifies 03 gram, or milligrams. The default worth of scale is ” 0″ (zero), simply because 00 . Lastly, the optional multiplier attribute may be applied to multiply the sort unit by a realnumbered aspect; this PubMed ID:https://www.ncbi.nlm.nih.gov/pubmed/19054792 enables the VU0361737 site definition of units which can be not poweroften multiples of SI units. As an illustration, a multiplier of 0.3048 could be made use of to define ” foot” as a measure of length when it comes to a metre. The multiplier attribute features a default value of ” ” (1). The unit method allows model quantities to be expressed in units apart from the base units of Table . For analyses and computations, the customer from the model (be it a software program tool or even a human) will need to convert all model quantities to base SI units for purposes including verifying the consistency of units throughout the model. Suppose we commence with a quantity obtaining numerical worth y when expressed in units u. The relationship amongst y plus a quantity yb expressed in base units ub isAuthor Manuscript Author Manuscript Author Manuscript Author ManuscriptThe term within the parentheses around the righthand side is actually a aspect w for converting a quantity in units u to an additional quantity in units ub. The ratio of units results in canceling of u inside the equation above and leaves a quantity in units ub. It remains to define this element. In terms of the SBML unit method, it can be: (2)where the dot ( represents easy scalar multiplication. The variables multiplier, scale, and exponent within the equation above correspond towards the attributes with the very same names inside the Unit object defined in Figure 2. The exponent inside the equation above might make it far more hard to grasp the connection straight away; so let us suppose for the moment that exponent” “. Then, it is effortless to determine thatJ Integr Bioinform. Author manuscript; readily available in PMC 207 June 02.Hucka et al.PageAuthor Manuscript Author Manuscript Author Manuscript Author ManuscriptDividing both sides by u produces the ratio inside the parenthesized portion of Equation , which means that w multiplier 0scale. To take a concrete example, one foot expressed with regards to the metre (a base unit) needs multiplier” 0.3048″, exponent” “, and scale” 0″:major to a conversion amongst quantities ofGiven a quantity of, say, y two, the conversion outcomes in yb 0.6096. To relate this to SBML terms a lot more concretely, the following fragment of SBML illustrates how this can be represented using the Unit and UnitDefinition constructs:The case above would be the simplest feasible circumstance, involving the transformation of quantities from a single defined unit u into a quantity expressed within a single base unit ub. If, instead, a number of base units ub, ub2, .. ubn are involved, the following equation holds (exactly where the mi terms are the multiplier values, the si terms will be the scale values, along with the xi terms will be the exponent values):(3)Application developers really should take care to track the exponents very carefully simply because they could be negative integers. The general use of Equation three is analogous to that of Equation 2, and results in the following final expression. Very first, to simplify, le.
