On the path structure of a semimartingale arising from monotone probability theory

Let X be the unique normal martingale such that X_0 = 0 and d[X]_t = (1 - t - X_{t-}) dX_t + dt and let Y_t := X_t + t for all t >= 0; the semimartingale Y arises in quantum probability, where it is the monotone-independent analogue of the Poisson process. The trajectories of Y are examined and various probabilistic properties are derived; in particular, the level set {t >= 0 : Y_t = 1} is shown to be non-empty, compact, perfect and of zero Lebesgue measure. The local times of Y are found to be trivial except for that at level 1; consequently, the jumps of Y are not locally summable

Quantum Feynman-Kac perturbations

We develop fully noncommutative Feynman-Kac formulae by employing quantum stochastic processes. To this end we establish some theory for perturbing quantum stochastic flows on von Neumann algebras by multiplier cocycles. Multiplier cocycles are constructed via quantum stochastic differential equations whose coefficients are driven by the flow. The resulting class of cocycles is characterised under alternative assumptions of separability or Markov regularity. Our results generalise those obtained using classical Brownian motion on the one hand, and results for unitarily implemented flows on the other.Comment: 27 pages. Minor corrections to version 2. To appear in the Journal of the London Mathematical Societ

A matrix formulation of quantum stochastic calculus

We develop the theory of chaos spaces and chaos matrices. A chaos space is a Hilbert space with a fixed, countably-infinite, direct-sum decomposition. A chaos matrix between two chaos spaces is a doubly-infinite matrix of bounded operators which respects this decomposition. We study operators represented by such matrices, particularly with respect to self-adjointness. This theory is used to re-formulate the quantum stochastic calculus of Hudson and Parthasarathy. Integrals of chaos-matrix processes are defined using the Hitsuda-Skorokhod integral and Malliavin gradient,following Lindsay and Belavkin. A new way of defining adaptedness is developed and the consequent quantum product Ito formula is used to provide a genuine functional Ito formula for polynomials in a large class of unbounded processes, which include the Poisson process and Brownian motion. A new type of adaptedness, known as $\Omega$-adaptedness, is defined. We show that quantum stochastic integrals of $\Omega$-adapted processes are well-behaved; for instance, bounded processes have bounded integrals. We solve the appropriate modification of the evolution equation of Hudson and Parthasarathy: $U(t)=I+\int_{0}^{t}E(s)\mathrm{d}\Lambda(s)+F(s)\mathrm{d} A(s)+ G(s)U(s)\mathrm{d} A^{\dagger}(s)+H(s)U(s)\mathrm{d} s,$ where the coefficients are time-dependent, bounded, $\Omega$-adapted processes acting on the whole Fock space. We show that the usual conditions on the coefficients, viz. (E,F,G,H)=(W-I,L,-WL^{*},iK+\mbox{\frac{1}{2}}LL^{*}) where $W$ is unitary and $K$ self-adjoint, are necessary and sufficient conditions for the solution to be unitary. This is a very striking result when compared to the adapted case

Spectra of comet P/Halley at R = 4 - 8 AU

Spectra of Comet Halley (lambda lambda = 3400-6500 A) were acquired at pre- and post-perihelion distances of 4.8 AU on 1985 Feb. 17 (Coma V equals 18.9 mag) and 1987 Feb. 1 (coma V = 15.9 mag) using the 4.5-m Multiple-Mirror Telescope (MMT) and the CTIO 4.0-m telescope, respectively. The CN(0,0) violet system band flux at 4.8 AU was approx. 15 times greater at the post-perhelion phase compared to pre-perihelion. Additional post-perihelion spectra, obtained on 1986 Nov. 28 to 30 with the MTT, showed CN(0,0) and very weak C3 4040 A emission. The MMT data are one-dimensional spectra (aperture: 5 arc sec diameter) obtained with an intensified Reticon while the CTIO data are two-dimensional spectra (slit length = 280 arc sec) obtained with a 2D-Frutti photon counting system. Extended CN(0,0) emission was detected in the 1987 Feb. 1 (at 4.8 AU) spectra to a distance of at least 70 arc sec in the solar and anti-solar directions. Additional CCD spectra obtained with the KPNO 2.2-meter telescope on 1988 Feb. 20 (at 7.9 AU) show scattered solar continuum approx. 32 arc sec diameter. However, no emission features were detected at 7.9 AU

Not just for the wealthy: Rethinking farmed fish consumption in the Global South

Aquaculture’s contributions to food security in the Global South are widely misunderstood. Dominant narratives suggest that aquaculture contributes mainly to international trade benefiting richer Northern consumers, or provides for wealthy urban consumers in Southern markets. On the supply side, the literature promotes an idealized vision of ‘small-scale’, low input, semi-subsistence farming as the primary means by which aquaculture can contribute to food security, or emphasizes the role of ‘industrial’ export oriented aquaculture in undermining local food security. In fact, farmed fish is produced predominantly by a ‘missing middle’ segment of commercial and increasingly intensive farms, and overwhelmingly remains in Southern domestic markets for consumption by poor and middle income consumers in both urban and rural areas, making an important but underappreciated contribution to global food security

Let them eat carp: Fish farms are helping to fight hunger

First paragraph: Over the past three decades, the global aquaculture industry has risen from obscurity to become a critical source of food for millions of people. In 1990, only 13 percent of world seafood consumption was farmed; by 2014, aquaculture was providing more than half of the fish consumed directly by human beings.  The boom has made farmed fish like shrimp, tilapia and pangasius catfish – imported from countries such as Thailand, China and Vietnam – an increasingly common sight in European and North American supermarkets. As a result, much research on aquaculture has emphasized production for export.  This focus has led scholars to question whether aquaculture contributes to the food security of poorer people in producing countries. Many have concluded it does not. Meanwhile, the industry’s advocates often emphasize the potential for small-scale farms, mainly growing fish for home consumption, to feed the poor. Farms of this kind are sometimes claimed to account for 70 to 80 percent of global aquaculture production

Mussel adhesive protein inspired coatings: a versatile method to fabricate silica films on various surfaces

A simple and versatile biomimetic strategy for the fabrication of silica films on a variety of substrates including gold, polystyrene and silicon wafers was developed using nanogram amounts per cm 2 of silicatein. The strategy exploits the adhesive property of 3,4-dihydroxyphenylalanine (DOPA) and a decapeptide (Ala-Lys-Pro-Ser-Tyr-DHP-Hyp-Thr-DOPA-Lys), important components of mussel adhesive proteins, to modify the surface of substrates. DOPA molecules polymerize to poly(DOPA) and the decapeptide forms thin films on gold substrates at pH 8.5, rendering the substrate compatible for silicatein immobilization. Nearly 50 ng cm 2 of silicatein is immobilized on poly(DOPA) and decapeptide coated surfaces where these polymer films act as "cushion" to protect the active structure and maintain the activity of the largely chemically adsorbed silicatein at ca. 95% of that experienced in solution. Uniform silica films of thickness 130-140 nm and roughness 12-14.5 nm were fabricated on coated gold surfaces. Evidence to show that this method is also applicable for the fabrication of uniform silica films on polystyrene and silicon substrates over multiple length scales in an economical way is also presented

Orientale and South Pole-Aitken basins on the Moon: Preliminary Galileo imaging results

During the Earth-Moon flyby the Galileo Solid State Imaging System obtained new information on the landscape and physical geology of the Moon. Multicolor Galileo images of the Moon reveal variations in color properties of the lunar surface. Using returned lunar samples as a key, the color differences can be interpreted in terms of variations in the mineral makeup of the lunar rocks and soil. The combined results of Apollo landings and multicolor images from Galileo allow extrapolation of surface composition to areas distant from the landing sites, including the far side invisible from Earth