The Future of Mathematics in Economics: A Philosophically Grounded Proposal

The use of mathematics in economics has been widely discussed. The philosophical discussion on what mathematics is remains unsettled on why it can be applied to the study of the real world. We propose to get back to some philosophical conceptions that lead to a language-like role for the mathematical analysis of economic phenomena and present some problems of interest that can be better examined in this light. Category theory provides the appropriate tools for these analytical approach.     

First record of a non-pollinating fig wasp (Hymenoptera: Sycophaginae) from Dominican amber,with estimation of the size of its host figs

Fig trees and their pollinating fig wasps arose about 75 million years ago in the Cretaceous period. Several other groups of chalcid wasps also utilize figs for larval development, including sycophagines, the putative sister group to pollinating fig wasps. Whereas stone and amber fossil pollinators are known, no fossils representing non-pollinating fig wasp groups have been confirmed previously. Here, we describe the first Sycophaginae from the c.15–20 Ma Dominican amber, Idarnes thanatos sp. nov. Farache, Rasplus, Pereira and Compton, and discuss its relationships within the Idarnes carme species group. Additionally, we use linear regression to compare body size, ovipositor sheaths length, and host fig size data from extant Idarnes species to estimate the size of its host figs. Idarnes thanatos was most likely associated with small to medium sized figs (diameter ≤1.0 cm), that were likely to have been dispersed by birds and primates. The discovery of this close relative of extant non-pollinating fig wasps suggests that early Miocene and modern fig wasp communities may share similar ecological and functional features.     

Kinetic approach to the study of froth flotation applied to a lepidolite ore

The number of published studies related to the optimization of lithium extraction from low-grade ores has increased as the demand for lithium has grown. However, no study related to the kinetics of the concentration stage of lithium-containing minerals by froth flotation has yet been reported. To establish a factorial design of batch flotation experiments, we conducted a set of kinetic tests to determine the most selective alternative collector, define a range of pulp pH values, and estimate a near-optimum flotation time. Both collectors (Aeromine 3000C and Armeen 12D) provided the required flotation selectivity, although this selectivity was lost in the case of pulp pH values outside the range between 2 and 4. Cumulative mineral recovery curves were used to adjust a classical kinetic model that was modified with a non-negative parameter representing a delay time. The computation of the near-optimum flotation time as the maximizer of a separation efficiency (SE) function must be performed with caution. We instead propose to define the near-optimum flotation time as the time interval required to achieve 95%–99% of the maximum value of the SE function.     

Spatial patterns of the semi-aquatic rodent Nectomys squamipes in Atlantic forest streams

Nectomys squamipes is a semi-aquatic rodent with a wide geographic range in Brazilian forests and savannas. This species is a host for several parasites associated with aquatic environments, especially Schistosoma mansoni, and thus its spatial pattern may influence some diseases’ patterns. Here we present important aspects of water rat spatial behaviour, including technical and ecological aspects. Water rats were studied by live trapping in rivers and in gallery forests between January 2005 and August 2008, with a total sampling effort of 9511 trap-nights. We also studied some animals through radio tracking and the spool-and-line technique. Water rat movement was distributed evenly between the terrestrial and aquatic environments. Nectomys squamipes occurrence in small tributaries was higher than in larger and lotic rivers. Both home range, the conventional two-dimensional approach, and home length, a one-dimensional approach, proved to be useful to study N. squamipes, depending on the shape of the water body used by the individual. Although Nectomys squamipes’ home length was positively correlated with body weight, sex was also important to explain home length variation; at similar body weights, males have larger home lengths than females. Males explored larger areas during the rainy season, likely in search of females, as this is the water rat reproductive season in Atlantic forest. In contrast, females explored larger areas during the dry season, likely looking for additional food supplies as a result of deficient water rat food supplies during the Atlantic forest dry season. Females overlapped home lengths with more than one male, and males with more than one female, suggesting a promiscuous mating system for this species.     

Optimization of an innovative approach involving mechanical activation and acid digestion for the extraction of lithium from lepidolite

The recovery of lithium from hard rock minerals has received increased attention given the high demand for this element. Therefore, this study optimized an innovative process, which does not require a high-temperature calcination step, for lithium extraction from lepidolite. Mechanical activation and acid digestion were suggested as crucial process parameters, and experimental design and response-surface methodology were applied to model and optimize the proposed lithium extraction process. The promoting effect of amorphization and the formation of lithium sulfate hydrate on lithium extraction yield were assessed. Several factor combinations led to extraction yields that exceeded 90%, indicating that the proposed process is an effective approach for lithium recovery.     

On differential structures of polynomial spaces in control theory

A valuable number of works has been published about Hurwitz and Schur polynomials in order to known better their properties.For example it is known that the sets of Hurwitz and Schur polynomials are open and no convex sets.Besides,the set of monic Schur polynomials is contractible.Now we study this set using ideas from differential topology,and we prove that the space of Schur complex polynomials with positive leading coefficient,and the space of Hurwitz complex polynomials which leading coefficient having positive real part,have structure of trivial vector bundle,and each space of (Schur complex and real,Hurwitz complex) polynomials has a differential structure diffeomorphic to some known spaces.     

A truncating mutation of HDAC2 in human cancers confers resistance to histone deacetylase inhibition

Disruption of histone acetylation patterns is a common feature of cancer cells, but very little is known about its genetic basis. We have identified truncating mutations in one of the primary human histone deacetylases, HDAC2, in sporadic carcinomas with microsatellite instability and in tumors arising in individuals with hereditary nonpolyposis colorectal cancer syndrome. The presence of the HDAC2 frameshift mutation causes a loss of HDAC2 protein expression and enzymatic activity and renders these cells more resistant to the usual antiproliferative and proapoptotic effects of histone deacetylase inhibitors. As such drugs may serve as therapeutic agents for cancer, our findings support the use of HDAC2 mutational status in future pharmacogenetic treatment of these individuals.