A Real Nullstellensatz for Matrices of Non-Commutative Polynomials

This article extends the classical Real Nullstellensatz to matrices of polynomials in a free $\ast$-algebra \RR\axs with $x=(x_1, \ldots, x_n)$. This result is a generalization of a result of Cimpri\vc, Helton, McCullough, and the author. In the free left \RR\axs-module \RR^{1 \times \ell}\axs we introduce notions of the (noncommutative) zero set of a left \RR\axs-submodule and of a real left \RR\axs-submodule. We prove that every element from \RR^{1 \times \ell}\axs whose zero set contains the intersection of zero sets of elements from a finite subset S \subset \RR^{1 \times \ell}\axs belongs to the smallest real left \RR\axs-submodule containing $S$. Using this, we derive a nullstellensatz for matrices of polynomials in \RR\axs. The other main contribution of this article is an efficient, implementable algorithm which for every finite subset S \subset \RR^{1 \times \ell}\axs computes the smallest real left \RR\axs-submodule containing $S$. This algorithm terminates in a finite number of steps. By taking advantage of the rigid structure of \RR\axs, the algorithm presented here is an improvement upon the previously known algorithm for \RR\axs

Sedimentation in an artificial lake -Lake Matahina, Bay of Plenty

Lake Matahina, an 8 km long hydroelectric storage reservoir, is a small (2.5 km2), 50 m deep, warm monomictic, gorge-type lake whose internal circulation is controlled by the inflowing Rangitaiki River which drains a greywacke and acid volcanic catchment. Three major proximal to distal subenvironments are defined for the lake on the basis of surficial sediment character and dominant depositional process: (a) fluvial-glassy, quartzofeld-spathic, and lithic gravel-sand mixtures deposited from contact and saltation loads in less than 3 m depth; (b) (pro-)deltaic-quartzofeldspathic and glassy sand-silt mixtures deposited from graded and uniform suspension loads in 3-20 m depth; and (c) basinal-diatomaceous, argillaceous, and glassy silt-clay mixtures deposited from uniform and pelagic suspension loads in 20-50 m depth. The delta face has been prograding into the lake at a rate of 35-40 m/year and vertical accretion rates in pro-delta areas are 15-20 cm/year. Basinal deposits are fed mainly from river plume dispersion involving overflows, interflows, and underflows, and by pelagic settling, and sedimentation rates behind the dam have averaged about 2 cm/year. Occasional fine sand layers in muds of basinal cores attest to density currents or underflows generated during river flooding flowing the length of the lake along a sublacustrine channel marking the position of the now submerged channel of the Rangitaiki River

Fiscal federalism and prospects for metropolitan transportation authorities in Portugal

Fiscal federalism refers to the attribution of public finance functions among different levels of government. We examine Portugal's metropolitan transportation sector through the fiscal federalist lens, in light of the country's decentralization efforts and new relevant legislation. We clarify basic principles of fiscal federalism and adapt them to the finance of metropolitan transportation systems – typically characterized by multiple jurisdictions, numerous externalities and equity concerns – showing the inadequacy of general practice. Portugal's overall public finance system partially adheres to fiscal federalist principles; the transportation sector less so. Metropolitan transportation faces particular troubles, with few direct user fees, prices inadequately reflecting costs, and heavy reliance on central government subsidies for public transportation investments and operations. A new law creating metropolitan transportation authorities is only modestly consistent with fiscal federalist principles, since it inadequately details financial responsibilities and remains under heavy central government control. Absent additional reforms, the new metropolitan authorities should aim to make the transportation finance system explicit and test incentive grants to induce inter-municipal cooperation.MIT Portugal Progra

E-cadherin engagement stimulates proliferation via Rac1

E-cadherin has been linked to the suppression of tumor growth and the inhibition of cell proliferation in culture. We observed that progressively decreasing the seeding density of normal rat kidney-52E (NRK- 52E) or MCF-10A epithelial cells from confluence, indeed, released cells from growth arrest. Unexpectedly, a further decrease in seeding density so that cells were isolated from neighboring cells decreased proliferation. Experiments using microengineered substrates showed that E-cadherin engagement stimulated the peak in proliferation at intermediate seeding densities, and that the proliferation arrest at high densities did not involve E-cadherin, but rather resulted from a crowding-dependent decrease in cell spreading against the underlying substrate. Rac1 activity, which was induced by E-cadherin engagement specifically at intermediate seeding densities, was required for the cadherin-stimulated proliferation, and the control of Rac1 activation by E-cadherin was mediated by p120- catenin. Together, these findings demonstrate a stimulatory role for E-cadherin in proliferative regulation, and identify a simple mechanism by which cell–cell contact may trigger or inhibit epithelial cell proliferation in different settings

Msn2 coordinates a stoichiometric gene expression program.

BackgroundMany cellular processes operate in an "analog" regime in which the magnitude of the response is precisely tailored to the intensity of the stimulus. In order to maintain the coherence of such responses, the cell must provide for proportional expression of multiple target genes across a wide dynamic range of induction states. Our understanding of the strategies used to achieve graded gene regulation is limited.ResultsIn this work, we document a relationship between stress-responsive gene expression and the transcription factor Msn2 that is graded over a large range of Msn2 concentrations. We use computational modeling and in vivo and in vitro analyses to dissect the roots of this relationship. Our studies reveal a simple and general strategy based on noncooperative low-affinity interactions between Msn2 and its cognate binding sites as well as competition over a large number of Msn2 binding sites in the genome relative to the number of Msn2 molecules.ConclusionsIn addition to enabling precise tuning of gene expression to the state of the environment, this strategy ensures colinear activation of target genes, allowing for stoichiometric expression of large groups of genes without extensive promoter tuning. Furthermore, such a strategy enables precise modulation of the activity of any given promoter by addition of binding sites without altering the qualitative relationship between different genes in a regulon. This feature renders a given regulon highly "evolvable.

Superior infectivity for mosquito vectors contributes to competitive displacement among strains of dengue virus

<p>Abstract</p> <p>Background</p> <p>Competitive displacement of a weakly virulent pathogen strain by a more virulent strain is one route to disease emergence. However the mechanisms by which pathogens compete for access to hosts are poorly understood. Among vector-borne pathogens, variation in the ability to infect vectors may effect displacement. The current study focused on competitive displacement in dengue virus serotype 3 (DENV3), a mosquito-borne pathogen of humans. In Sri Lanka in the 1980's, a native DENV3 strain associated with relatively mild dengue disease was displaced by an invasive DENV3 strain associated with the most severe disease manifestations, dengue hemorrhagic fever/dengue shock syndrome (DHF/DSS), resulting in an outbreak of DHF/DSS. Here we tested the hypothesis that differences between the invasive and native strain in their infectivity for <it>Aedes aegypti </it>mosquitoes, the primary vector of DENV, contributed to the competitive success of the invasive strain</p> <p>Results</p> <p>To be transmitted by a mosquito, DENV must infect and replicate in the midgut, disseminate into the hemocoel, infect the salivary glands, and be released into the saliva. The ability of the native and invasive DENV3 strains to complete the first three steps of this process in <it>Aedes aegypti </it>mosquitoes was measured <it>in vivo</it>. The invasive strain infected a similar proportion of mosquitoes as the native strain but replicated to significantly higher titers in the midgut and disseminated with significantly greater efficiency than the native strain. In contrast, the native and invasive strain showed no significant difference in replication in cultured mosquito, monkey or human cells.</p> <p>Conclusion</p> <p>The invasive DENV3 strain infects and disseminates in <it>Ae. aegypti </it>more efficiently than the displaced native DENV3 strain, suggesting that the invasive strain is transmitted more efficiently. Replication in cultured cells did not adequately characterize the known phenotypic differences between native and invasive DENV3 strains. Infection dynamics within the vector may have a significant impact on the spread and replacement of dengue virus lineages.</p