The Principle of Similitude in Biology: From Allometry to the Formulation of Dimensionally Homogenous `Laws'

Meaningful laws of nature must be independent of the units employed to measure the variables. The principle of similitude (Rayleigh 1915) or dimensional homogeneity, states that only commensurable quantities (ones having the same dimension) may be compared, therefore, meaningful laws of nature must be homogeneous equations in their various units of measurement, a result which was formalized in the $\rm \Pi$ theorem (Vaschy 1892; Buckingham 1914). However, most relations in allometry do not satisfy this basic requirement, including the `3/4 Law' (Kleiber 1932) that relates the basal metabolic rate and body mass, which it is sometimes claimed to be the most fundamental biological rate (Brown et al. 2004) and the closest to a law in life sciences (West \& Brown 2004). Using the $\rm \Pi$ theorem, here we show that it is possible to construct a unique homogeneous equation for the metabolic rates, in agreement with data in the literature. We find that the variations in the dependence of the metabolic rates on body mass are secondary, coming from variations in the allometric dependence of the heart frequencies. This includes not only different classes of animals (mammals, birds, invertebrates) but also different exercise conditions (basal and maximal). Our results demonstrate that most of the differences found in the allometric exponents (White et al. 2007) are due to compare incommensurable quantities and that our dimensionally homogenous formula, unify these differences into a single formulation. We discuss the ecological implications of this new formulation in the context of the Malthusian's, Fenchel's and the total energy consumed in a lifespan relations.Comment: A accepted for publication in Theoretical Ecology. Comments are welcome ([email protected]

Gravitational Fragmentation in Galaxy Mergers: A Stability Criteria

We study the gravitational stability of gaseous streams in the complex environment of a galaxy merger, because mergers are known to be places of ongoing massive cluster formation and bursts of star formation. We find an analytic stability parameter for case of gaseous streams orbiting around the merger remnant. We test our stability criteria using hydrodynamical simulations of galaxy mergers, obtaining satisfactory results. We find that our criteria successfully predicts the streams that will be gravitationally unstable to fragment into clumps.Comment: 10 pages, 2 figures. After 2nd referee repor

A CASE STUDY OF LUNTIAN MULTI-PURPOSE COOPERATIVE IN BARANGAY LALAIG, TIAONG, QUEZON, PHILIPPINES: A VERTICAL INTEGRATION APPROACH

The Luntian Multi-Purpose Cooperative located in Tiaong, Quezon, Philippines. The Luntian Multi-Purpose cooperative focuses more on feed production as well as hog fattening. The LMC applied the vertical integration to develop the cooperative. They have their members as their primary costumers of their feeds. The cooperative’s business activity includes also meat shop, granting of production loan, micro-finance, mobilization of saving deposits, aside from feed milling and hog fattening. Different agencies, industry organizations and private institutions provide trainings, seminars, assistance, as well as credit for the cooperative.The aims of the study was to determine the present and discuss a noteworthy business issue (s) of Luntian Multipurpose Cooperative, evaluate the business environment prevailing at a particular time of this case , assess the cooperative’s performance in terms of the four business functions , define the problem relevant to the business issue(s) being studied. The study used primary and secondary data. Primary data were gathered through interviews with the key personnel, managers, and other informants of the Luntian Multipurpose Cooperative in order to obtain responses regarding the overall status of the cooperative including its problem and plans. Secondary data were taken from files and documents, especially the history, background information and financial statements. Other data were taken through research materials such as book, unpublished special problems and from some government institutions. The recommendation of this research showed that Luntian MPC should engage in establishing a communal farm as to become the primary source of hybrid piglets that their members would raised. The alternatives solution was establishing a breeding farm that would ask for initial investment. Keywords: cooperative, vertical integration, case study, por

Vitis catalana: una eina per a documentar les varietats de ceps presents als territoris de parla catalana

Vitis Catalana és una eina de consulta en línia que vol agrupar les notícies sobre varietats de vinya catalanes que han aparegut al llarg de la història en documents de tipologia molt diversa. S'ha inspirat en el «Fitxer general de varietats de ceps» elaborat per l'historiador Emili Giralt i Raventós, del qual ha pres la idea i les gairebé quinze mil fitxes manuscrites que el conformen. El seu objectiu és facilitar l'estudi de les varietats tradicionals cultivades en els territoris de parla i cultura catalanes.Vitis Catalana is an online database that includes historical mentions made in diverse types of documents about Catalan vine varieties. It was inspired by the general File of vine varieties developed by the historian Emili Giralt i Raventós, which includes almost 15,000 handwritten cards. Its aim is to facilitate the study of traditional varieties grown in the Catalan language and culture area.Vitis Catalana es una herramienta de consulta on line que contiene las noticias sobre variedades de viña catalanas que han aparecido a lo largo de la historia en documentos de tipología muy diversa. Se ha inspirado en el «Fichero general de variedades de cepas» elaborado por el historiador Emili Giralt i Raventós, del cual se ha tomado la idea y las casi quince mil fichas manuscritas que lo conforman. Su objetivo es facilitar el estudio de las variedades tradicionales cultivadas en los territorios de habla y cultura catalana