Superposition: on Cavalieri’s practice of mathematics

Bonaventura Cavalieri has been the subject of numerous scholarly publications. Recent students of Cavalieri have placed his geometry of indivisibles in the context of early modern mathematics, emphasizing the role of new geometrical objects, such as, for example, linear and plane indivisibles. In this paper, I will complement this recent trend by focusing on how Cavalieri manipulates geometrical objects. In particular, I will investigate one fundamental activity, namely, superposition of geometrical objects. In Cavalieri’s practice, superposition is a means of both manipulating geometrical objects and drawing inferences. Finally, I will suggest that an integrated approach, namely, one which strives to understand both objects and activities, can illuminate the history of mathematics.     

Radical mathematical Thomism: beings of reason and divine decrees in Torricelli’s philosophy of mathematics

Evangelista Torricelli (1608-1647) is perhaps best known for being the most gifted of Galileo’s pupils, and for his works based on indivisibles, especially his stunning cubature of an infinite hyperboloid. Scattered among Torricelli’s writings, we find numerous traces of the philosophy of mathematics underlying his mathematical practice. Though virtually neglected by historians and philosophers alike, these traces reveal that Torricelli’s mathematical practice was informed by an original philosophy of mathematics. The latter was dashed with strains of Thomistic metaphysics and theology. Torricelli’s philosophy of mathematics emphasized mathematical constructs as human-made beings of reason, yet mathematical truths as divine decrees, which upon being discovered by the mathematician ‘appropriate eternity’. In this paper, I reconstruct Torricelli’s philosophy of mathematics—which I label radical mathematical Thomism—placing it in the context of Thomistic patterns of thought.     

A Fuzzy Clustering Model for Multivariate Spatial Time Series

Clustering of multivariate spatial-time series should consider: 1) the spatial nature of the objects to be clustered; 2) the characteristics of the feature space, namely the space of multivariate time trajectories; 3) the uncertainty associated to the assignment of a spatial unit to a given cluster on the basis of the above complex features. The last aspect is dealt with by using the Fuzzy C-Means objective function, based on appropriate measures of dissimilarity between time trajectories, by distinguishing the cross-sectional and longitudinal aspects of the trajectories. In order to take into account the spatial nature of the statistical units, a spatial penalization term is added to the above function, depending on a suitable spatial proximity/ contiguity matrix. A tuning coefficient takes care of the balance between, on one side, discriminating according to the pattern of the time trajectories and, on the other side, ensuring an approximate spatial homogeneity of the clusters. A technique for determining an optimal value of this coefficient is proposed, based on an appropriate spatial autocorrelation measure. Finally, the proposed models are applied to the classification of the Italian provinces, on the basis of the observed dynamics of some socio-economical indicators.     

Comparative genomics of the neglected human malaria parasite Plasmodium vivax

The human malaria parasite Plasmodium vivax is responsible for 25-40% of the approximately 515 million annual cases of malaria worldwide. Although seldom fatal, the parasite elicits severe and incapacitating clinical symptoms and often causes relapses months after a primary infection has cleared. Despite its importance as a major human pathogen, P. vivax is little studied because it cannot be propagated continuously in the laboratory except in non-human primates. We sequenced the genome of P. vivax to shed light on its distinctive biological features, and as a means to drive development of new drugs and vaccines. Here we describe the synteny and isochore structure of P. vivax chromosomes, and show that the parasite resembles other malaria parasites in gene content and metabolic potential, but possesses novel gene families and potential alternative invasion pathways not recognized previously. Completion of the P. vivax genome provides the scientific community with a valuable resource that can be used to advance investigation into this neglected species.     

A fundamental avian wing-stroke provides a new perspective on the evolution of flight

The evolution of avian flight remains one of biology's major controversies, with a long history of functional interpretations of fossil forms given as evidence for either an arboreal or cursorial origin of flight. Despite repeated emphasis on the 'wing-stroke' as a necessary avenue of investigation for addressing the evolution of flight, no empirical data exist on wing-stroke dynamics in an experimental evolutionary context. Here we present the first comparison of wing-stroke kinematics of the primary locomotor modes (descending flight and incline flap-running) that lead to level-flapping flight in juvenile ground birds throughout development. We offer results that are contrary both to popular perception and inferences from other studies. Starting shortly after hatching and continuing through adulthood, ground birds use a wing-stroke confined to a narrow range of less than 20 degrees , when referenced to gravity, that directs aerodynamic forces about 40 degrees above horizontal, permitting a 180 degrees range in the direction of travel. Based on our results, we put forth an ontogenetic-transitional wing hypothesis that posits that the incremental adaptive stages leading to the evolution of avian flight correspond behaviourally and morphologically to transitional stages observed in ontogenetic forms.     

Six unidentified reading frames of human mitochondrial DNA encode components of the respiratory-chain NADH dehydrogenase

The products of six unidentified reading frames of human mitochondrial DNA are precipitated from a mitochondrial lysate by antibodies against highly purified native beef heart NADH-ubiquinone oxidoreductase (complex I). These products are enriched greatly in a human submitochondrial fraction enriched in NADH-Q1 and NADH-K3Fe(CN)6 oxidoreductase activities. We conclude that the six reading frames encode components of the respiratory-chain NADH dehydrogenase.     

PML inhibits HIF-1alpha translation and neoangiogenesis through repression of mTOR

Loss of the promyelocytic leukaemia (PML) tumour suppressor has been observed in several human cancers. The tumour-suppressive function of PML has been attributed to its ability to induce growth arrest, cellular senescence and apoptosis. Here we identify PML as a critical inhibitor of neoangiogenesis (the formation of new blood vessels) in vivo, in both ischaemic and neoplastic conditions, through the control of protein translation. We demonstrate that in hypoxic conditions PML acts as a negative regulator of the synthesis rate of hypoxia-inducible factor 1alpha (HIF-1alpha) by repressing mammalian target of rapamycin (mTOR). PML physically interacts with mTOR and negatively regulates its association with the small GTPase Rheb by favouring mTOR nuclear accumulation. Notably, Pml-/- cells and tumours display higher sensitivity both in vitro and in vivo to growth inhibition by rapamycin, and lack of PML inversely correlates with phosphorylation of ribosomal protein S6 and tumour angiogenesis in mouse and human tumours. Thus, our findings identify PML as a novel suppressor of mTOR and neoangiogenesis.     

The genome of the protist parasite Entamoeba histolytica

Entamoeba histolytica is an intestinal parasite and the causative agent of amoebiasis, which is a significant source of morbidity and mortality in developing countries. Here we present the genome of E. histolytica, which reveals a variety of metabolic adaptations shared with two other amitochondrial protist pathogens: Giardia lamblia and Trichomonas vaginalis. These adaptations include reduction or elimination of most mitochondrial metabolic pathways and the use of oxidative stress enzymes generally associated with anaerobic prokaryotes. Phylogenomic analysis identifies evidence for lateral gene transfer of bacterial genes into the E. histolytica genome, the effects of which centre on expanding aspects of E. histolytica's metabolic repertoire. The presence of these genes and the potential for novel metabolic pathways in E. histolytica may allow for the development of new chemotherapeutic agents. The genome encodes a large number of novel receptor kinases and contains expansions of a variety of gene families, including those associated with virulence. Additional genome features include an abundance of tandemly repeated transfer-RNA-containing arrays, which may have a structural function in the genome. Analysis of the genome provides new insights into the workings and genome evolution of a major human pathogen.     

A continuum model for tumour suppression

This year, 2011, marks the forty-year anniversary of the statistical analysis of retinoblastoma that provided the first evidence that tumorigenesis can be initiated by as few as two mutations. This work provided the foundation for the two-hit hypothesis that explained the role of recessive tumour suppressor genes (TSGs) in dominantly inherited cancer susceptibility syndromes. However, four decades later, it is now known that even partial inactivation of tumour suppressors can critically contribute to tumorigenesis. Here we analyse this evidence and propose a continuum model of TSG function to explain the full range of TSG mutations found in cancer.     

Role of nucleophosmin in embryonic development and tumorigenesis

Nucleophosmin (also known as NPM, B23, NO38) is a nucleolar protein directly implicated in cancer pathogenesis, as the NPM1 gene is found mutated and rearranged in a number of haematological disorders. Furthermore, the region of chromosome 5 to which NPM1 maps is deleted in a proportion of de novo human myelodysplastic syndromes (MDS), and loss of chromosome 5 is extremely frequent in therapy-related MDS. NPM is a multifunctional protein, and its role in oncogenesis is controversial as NPM has been attributed with both oncogenic and tumour suppressive functions. To study the function of Npm in vivo, we generated a hypomorphic Npm1 mutant series (Npm1+/- < Npm1(hy/hy) < Npm1-/-) in mouse. Here we report that Npm is essential for embryonic development and the maintenance of genomic stability. Npm1-/- and Npm1(hy/hy) mutants have aberrant organogenesis and die between embryonic day E11.5 and E16.5 owing to severe anaemia resulting from defects in primitive haematopoiesis. We show that Npm1 inactivation leads to unrestricted centrosome duplication and genomic instability. We demonstrate that Npm is haploinsufficient in the control of genetic stability and that Npm1 heterozygosity accelerates oncogenesis both in vitro and in vivo. Notably, Npm1+/- mice develop a haematological syndrome with features of human MDS. Our findings uncover an essential developmental role for Npm and implicate its functional loss in tumorigenesis and MDS pathogenesis.