A Birkhoff connection between quantum circuits and linear classical reversible circuits

Birkhoff's theorem tells how any doubly stochastic matrix can be decomposed as a weighted sum of permutation matrices. Similar theorems on unitary matrices reveal a connection between quantum circuits and linear classical reversible circuits. It triggers the question whether a quantum computer can be regarded as a superposition of classical reversible computers

On two subgroups of U(n), useful for quantum computing

As two basic building blocks for any quantum circuit, we consider the 1-qubit PHASOR circuit Phi(theta) and the 1-qubit NEGATOR circuit N(theta). Both are roots of the IDENTITY circuit. Indeed: both (NO) and N(0) equal the 2 x 2 unit matrix. Additionally, the NEGATOR is a root of the classical NOT gate. Quantum circuits (acting on w qubits) consisting of controlled PHASORs are represented by matrices from ZU(2(w)); quantum circuits consisting of controlled NEGATORs are represented by matrices from XU(2(w)). Here, ZU(n) and XU(n) are subgroups of the unitary group U(n): the group XU(n) consists of all n x n unitary matrices with all 2n line sums (i.e. all n row sums and all n column sums) equal to 1 and the group ZU(n) consists of all n x n unitary diagonal matrices with first entry equal to 1. Any U(n) matrix can be decomposed into four parts: U = exp(i alpha) Z(1)XZ(2), where both Z(1) and Z(2) are ZU(n) matrices and X is an XU(n) matrix. We give an algorithm to find the decomposition. For n = 2(w) it leads to a four-block synthesis of an arbitrary quantum computer

Flux, Impact, and Fate of Halogenated Xenobiotic Compounds in the Gut

Humans and their associated microbiomes are exposed to numerous xenobiotics through drugs, dietary components, personal care products as well as environmental chemicals. Most of the reciprocal interactions between the microbiota and xenobiotics, such as halogenated compounds, occur within the human gut harboring diverse and dense microbial communities. Here, we provide an overview of the flux of halogenated compounds in the environment, and diverse exposure routes of human microbiota to these compounds. Subsequently, we review the impact of halogenated compounds in perturbing the structure and function of gut microbiota and host cells. In turn, cultivation-dependent and metagenomic surveys of dehalogenating genes revealed the potential of the gut microbiota to chemically alter halogenated xenobiotics and impact their fate. Finally, we provide an outlook for future research to draw attention and attract interest to study the bidirectional impact of halogenated and other xenobiotic compounds and the gut microbiota.Peer reviewe

The Kazhdan-Lusztig conjecture for W-algebras

The main result in this paper is the character formula for arbitrary irreducible highest weight modules of W algebras. The key ingredient is the functor provided by quantum Hamiltonian reduction, that constructs the W algebras from affine Kac-Moody algebras and in a similar fashion W modules from KM modules. Assuming certain properties of this functor, the W characters are subsequently derived from the Kazhdan-Lusztig conjecture for KM algebras. The result can be formulated in terms of a double coset of the Weyl group of the KM algebra: the Hasse diagrams give the embedding diagrams of the Verma modules and the Kazhdan-Lusztig polynomials give the multiplicities in the characters.Comment: uuencoded file, 29 pages latex, 5 figure

Reconstructing functional networks in the human intestinal tract using synthetic microbiomes : Systems Biology • Nanobiotechnology

The human intestinal tract harbors one of the most densely populated and open microbial ecosystems. The application of multi-omics approaches has provided insight into a wide array of complex interactions between the various groups of mainly anaerobic colonic microbes as well as the host-microbe dialogue. Integration of multi-omits techniques in cultivation based experiments that vary in complexity from monocultures to synthetic microbial communities identified key metabolic players in the trophic interactions as well as their ecological dynamics. A synergy between these approaches will be of utmost importance to reconstruct the functional interaction networks at the ecosystem level within the human intestinal microbiome. The improved understanding of microbiome functioning at ecosystem level will further aid in developing better predictive models and design of effective microbiome modulation strategies for health benefits.Peer reviewe

Cross-talk between signaling pathways leading to defense against pathogens and insects

In nature, plants interact with a wide range of organisms, some of which are harmful (e.g. pathogens, herbivorous insects), while others are beneficial (e.g. growth-promoting rhizobacteria, mycorrhizal fungi, and predatory enemies of herbivores). During the evolutionary arms race between plants and their attackers, primary and secondary immune responses evolved to recognize common or highly specialized features of microbial pathogens (Chisholm et al., 2006), resulting in sophisticated mechanisms of defense

Cosmic rays studied with a hybrid high school detector array

The LORUN/NAHSA system is a pathfinder for hybrid cosmic ray research combined with education and outreach in the field of astro-particle physics. Particle detectors and radio antennae were mainly setup by students and placed on public buildings. After fully digital data acquisition, coincidence detections were selected. Three candidate events confirmed a working prototype, which can be multiplied to extend further particle detector arrays on high schools.Comment: 10 pages, 6 figures. Nigl, A., Timmermans, C., Schellart, P., Kuijpers, J., Falcke, H., Horneffer, A., de Vos, C. M., Koopman, Y., Pepping, H. J., Schoonderbeek, G., Cosmic rays studied with a hybrid high school detector array, Europhysics News (EPN), Vol. 38, No. 5, accepted on 22/08/200