Analysis of linear trade models and relation to scale economies

We discuss linear Ricardo models with a range of parameters. We show that the exact boundary of the region of equilibria of these models is obtained by solving a simple integer programming problem. We show that there is also an exact correspondence between many of the equilibria resulting from families of linear models and the multiple equilibria of economies of scale models.

Coexistence of linear zones and pinwheels within orientation maps in cat visual cortex

Revealing the layout of cortical maps is important both for understanding the processes involved in their development and for uncovering the mechanisms underlying neural computation. The typical organization of orientation maps in the cat visual cortex is radial; complete orientation cycles are mapped around orientation singularities. In contrast, long linear zones of orientation representation have been detected in the primary visual cortex of the tree shrew. In this study, we searched for the existence of long linear sequences and wide linear zones within orientation preference maps of the cat visual cortex. Optical imaging based on intrinsic signals was used. Long linear sequences and wide linear zones of preferred orientation were occasionally detected along the border between areas 17 and 18, as well as within area 18. Adjacent zones of distinct radial and linear organizations were observed across area 18 of a single hemisphere. However, radial and linear organizations were not necessarily segregated; long (7.5 mm) linear sequences of preferred orientation were found embedded within a typical pinwheel-like organization of orientation. We conclude that, although the radial organization is dominant, perfectly linear organization may develop and perform the processing related to orientation in the cat visual cortex.

Cerebral organization for language in deaf and hearing subjects: Biological constraints and effects of experience

Cerebral organization during sentence processing in English and in American Sign Language (ASL) was characterized by employing functional magnetic resonance imaging (fMRI) at 4 T. Effects of deafness, age of language acquisition, and bilingualism were assessed by comparing results from (i) normally hearing, monolingual, native speakers of English, (ii) congenitally, genetically deaf, native signers of ASL who learned English late and through the visual modality, and (iii) normally hearing bilinguals who were native signers of ASL and speakers of English. All groups, hearing and deaf, processing their native language, English or ASL, displayed strong and repeated activation within classical language areas of the left hemisphere. Deaf subjects reading English did not display activation in these regions. These results suggest that the early acquisition of a natural language is important in the expression of the strong bias for these areas to mediate language, independently of the form of the language. In addition, native signers, hearing and deaf, displayed extensive activation of homologous areas within the right hemisphere, indicating that the specific processing requirements of the language also in part determine the organization of the language systems of the brain.

The underlying pathway structure of biochemical reaction networks

Bioinformatics is yielding extensive, and in some cases complete, genetic and biochemical information about individual cell types and cellular processes, providing the composition of living cells and the molecular structure of its components. These components together perform integrated cellular functions that now need to be analyzed. In particular, the functional definition of biochemical pathways and their role in the context of the whole cell is lacking. In this study, we show how the mass balance constraints that govern the function of biochemical reaction networks lead to the translation of this problem into the realm of linear algebra. The functional capabilities of biochemical reaction networks, and thus the choices that cells can make, are reflected in the null space of their stoichiometric matrix. The null space is spanned by a finite number of basis vectors. We present an algorithm for the synthesis of a set of basis vectors for spanning the null space of the stoichiometric matrix, in which these basis vectors represent the underlying biochemical pathways that are fundamental to the corresponding biochemical reaction network. In other words, all possible flux distributions achievable by a defined set of biochemical reactions are represented by a linear combination of these basis pathways. These basis pathways thus represent the underlying pathway structure of the defined biochemical reaction network. This development is significant from a fundamental and conceptual standpoint because it yields a holistic definition of biochemical pathways in contrast to definitions that have arisen from the historical development of our knowledge about biochemical processes. Additionally, this new conceptual framework will be important in defining, characterizing, and studying biochemical pathways from the rapidly growing information on cellular function.

Constraints on nebular dynamics and chemistry based on observations of annealed magnesium silicate grains in comets and in disks surrounding Herbig Ae/Be stars

Understanding dynamic conditions in the Solar Nebula is the key to prediction of the material to be found in comets. We suggest that a dynamic, large-scale circulation pattern brings processed dust and gas from the inner nebula back out into the region of cometesimal formation—extending possibly hundreds of astronomical units (AU) from the sun—and that the composition of comets is determined by a chemical reaction network closely coupled to the dynamic transport of dust and gas in the system. This scenario is supported by laboratory studies of Mg silicates and the astronomical data for comets and for protoplanetary disks associated with young stars, which demonstrate that annealing of nebular silicates must occur in conjunction with a large-scale circulation. Mass recycling of dust should have a significant effect on the chemical kinetics of the outer nebula by introducing reduced, gas-phase species produced in the higher temperature and pressure environment of the inner nebula, along with freshly processed grains with “clean” catalytic surfaces to the region of cometesimal formation. Because comets probably form throughout the lifetime of the Solar Nebula and processed (crystalline) grains are not immediately available for incorporation into the first generation of comets, an increasing fraction of dust incorporated into a growing comet should be crystalline olivine and this fraction can serve as a crude chronometer of the relative ages of comets. The formation and evolution of key organic and biogenic molecules in comets are potentially of great consequence to astrobiology.

Trapping of branched DNA in microfabricated structures.

We have observed electrostatic trapping of tribranched DNA molecules undergoing electrophoresis in a microfabricated pseudo-two-dimensional array of posts. Trapping occurs in a unique transport regimen in which the electrophoretic mobility is extremely sensitive to polymer topology. The arrest of branched polymers is explained by considering their center-of-mass motion; in certain conformations, owing to the constraints imposed by the obstacles a molecule cannot advance without the center of mass first moving a short distance backwards. The depth of the resulting local potential well can be much greater than the thermal energy so that escape of an immobilized molecule can be extremely slow. We summarize the expected behavior of the mobility as a function of field strength and topology and point out that the microfabricated arrays are highly suitable for detecting an extremely small number of branched molecules in a very large population of linear molecules.