Witnessing random unitary and projective quantum channels: Complementarity between separable and maximally entangled states

Modern applications in quantum computation and quantum communication require the precise characterization of quantum states and quantum channels. In practice, this means that one has to determine the quantum capacity of a physical system in terms of measurable quantities. Witnesses, if properly constructed, succeed in performing this task. We derive a method that is capable to compute witnesses for identifying deterministic evolutions and measurement-induced collapse processes. At the same time, applying the Choi-Jamiolkowski isomorphism, it uncovers the entanglement characteristics of bipartite quantum states. Remarkably, a statistical mixture of unitary evolutions is mapped onto mixtures of maximally entangled states, and classical separable states originate from genuine quantum-state reduction maps. Based on our treatment we are able to witness these opposing attributes at once and, furthermore, obtain an insight into their different geometric structures. The complementarity is further underpinned by formulating a complementary Schmidt decomposition of a state in terms of maximally entangled states and discrete Fourier-transformed Schmidt coefficients.Comment: close to published versio

Dispersal in microbes: fungi in indoor air are dominated by outdoor air and show dispersal limitation at short distances.

The indoor microbiome is a complex system that is thought to depend on dispersal from the outdoor biome and the occupants' microbiome combined with selective pressures imposed by the occupants' behaviors and the building itself. We set out to determine the pattern of fungal diversity and composition in indoor air on a local scale and to identify processes behind that pattern. We surveyed airborne fungal assemblages within 1-month time periods at two seasons, with high replication, indoors and outdoors, within and across standardized residences at a university housing facility. Fungal assemblages indoors were diverse and strongly determined by dispersal from outdoors, and no fungal taxa were found as indicators of indoor air. There was a seasonal effect on the fungi found in both indoor and outdoor air, and quantitatively more fungal biomass was detected outdoors than indoors. A strong signal of isolation by distance existed in both outdoor and indoor airborne fungal assemblages, despite the small geographic scale in which this study was undertaken (<500 m). Moreover, room and occupant behavior had no detectable effect on the fungi found in indoor air. These results show that at the local level, outdoor air fungi dominate the patterning of indoor air. More broadly, they provide additional support for the growing evidence that dispersal limitation, even on small geographic scales, is a key process in structuring the often-observed distance-decay biogeographic pattern in microbial communities

Four generated, squarefree, monomial ideals

Let $I\supsetneq J$ be two squarefree monomial ideals of a polynomial algebra over a field generated in degree $\geq d$, resp. $\geq d+1$ . Suppose that $I$ is either generated by three monomials of degrees $d$ and a set of monomials of degrees $\geq d+1$, or by four special monomials of degrees $d$. If the Stanley depth of $I/J$ is $\leq d+1$ then the usual depth of $I/J$ is $\leq d+1$ too.Comment: to appear in "Bridging Algebra, Geometry, and Topology", Editors Denis Ibadula, Willem Veys, Springer Proceed. in Math. and Statistics, 96, 201

(Bi-)Cohen-Macaulay simplicial complexes and their associated coherent sheaves

Via the BGG correspondence a simplicial complex Delta on [n] is transformed into a complex of coherent sheaves on P^n-1. We show that this complex reduces to a coherent sheaf F exactly when the Alexander dual Delta^* is Cohen-Macaulay. We then determine when both Delta and Delta^* are Cohen-Macaulay. This corresponds to F being a locally Cohen-Macaulay sheaf. Lastly we conjecture for which range of invariants of such Delta it must be a cone.Comment: 16 pages, some minor change

Citizen participation in news

The process of producing news has changed significantly due to the advent of the Web, which has enabled the increasing involvement of citizens in news production. This trend has been given many names, including participatory journalism, produsage, and crowd-sourced journalism, but these terms are ambiguous and have been applied inconsistently, making comparison of news systems difficult. In particular, it is problematic to distinguish the levels of citizen involvement, and therefore the extent to which news production has genuinely been opened up. In this paper we perform an analysis of 32 online news systems, comparing them in terms of how much power they give to citizens at each stage of the news production process. Our analysis reveals a diverse landscape of news systems and shows that they defy simplistic categorisation, but it also provides the means to compare different approaches in a systematic and meaningful way. We combine this with four case studies of individual stories to explore the ways that news stories can move and evolve across this landscape. Our conclusions are that online news systems are complex and interdependent, and that most do not involve citizens to the extent that the terms used to describe them imply

Governance for integrated water resources management in a river-basin context: proceedings of a regional seminar, Bangkok, May, 2002

Water resource management / River basins / Governance / Institutional development / Groundwater irrigation / Water policy / Water allocation / Water demand / Irrigation efficiency / Models / Case studies

Linear resolutions of powers and products

The goal of this paper is to present examples of families of homogeneous ideals in the polynomial ring over a field that satisfy the following condition: every product of ideals of the family has a linear free resolution. As we will see, this condition is strongly correlated to good primary decompositions of the products and good homological and arithmetical properties of the associated multi-Rees algebras. The following families will be discussed in detail: polymatroidal ideals, ideals generated by linear forms and Borel fixed ideals of maximal minors. The main tools are Gr\"obner bases and Sagbi deformation

Fungi isolated from Miscanthus and sugarcane: biomass conversion, fungal enzymes, and hydrolysis of plant cell wall polymers.

BackgroundBiofuel use is one of many means of addressing global change caused by anthropogenic release of fossil fuel carbon dioxide into Earth's atmosphere. To make a meaningful reduction in fossil fuel use, bioethanol must be produced from the entire plant rather than only its starch or sugars. Enzymes produced by fungi constitute a significant percentage of the cost of bioethanol production from non-starch (i.e., lignocellulosic) components of energy crops and agricultural residues. We, and others, have reasoned that fungi that naturally deconstruct plant walls may provide the best enzymes for bioconversion of energy crops.ResultsPreviously, we have reported on the isolation of 106 fungi from decaying leaves of Miscanthus and sugarcane (Appl Environ Microbiol 77:5490-504, 2011). Here, we thoroughly analyze 30 of these fungi including those most often found on decaying leaves and stems of these plants, as well as four fungi chosen because they are well-studied for their plant cell wall deconstructing enzymes, for wood decay, or for genetic regulation of plant cell wall deconstruction. We extend our analysis to assess not only their ability over an 8-week period to bioconvert Miscanthus cell walls but also their ability to secrete total protein, to secrete enzymes with the activities of xylanases, exocellulases, endocellulases, and beta-glucosidases, and to remove specific parts of Miscanthus cell walls, that is, glucan, xylan, arabinan, and lignin.ConclusionThis study of fungi that bioconvert energy crops is significant because 30 fungi were studied, because the fungi were isolated from decaying energy grasses, because enzyme activity and removal of plant cell wall components were recorded in addition to biomass conversion, and because the study period was 2 months. Each of these factors make our study the most thorough to date, and we discovered fungi that are significantly superior on all counts to the most widely used, industrial bioconversion fungus, Trichoderma reesei. Many of the best fungi that we found are in taxonomic groups that have not been exploited for industrial bioconversion and the cultures are available from the Centraalbureau voor Schimmelcultures in Utrecht, Netherlands, for all to use

Fermat hypersurfaces and Subcanonical curves

We extend the classical Enriques-Petri Theorem to $s$-subcanonical projectively normal curves, proving that such a curve is $(s+2)$-gonal if and only if it is contained in a surface of minimal degree. Moreover, we show that any Fermat hypersurface of degree $s+2$ is apolar to an $s$-subcanonical $(s+2)$-gonal projectively normal curve, and vice versa.Comment: 18 pages; AMS-LaTe