Universal Baxterization for Z\mathbb{Z}-graded Hopf algebras

We present a method for Baxterizing solutions of the constant Yang-Baxter equation associated with $\mathbb{Z}$-graded Hopf algebras. To demonstrate the approach, we provide examples for the Taft algebras and the quantum group $U_q[sl(2)]$.Comment: 8 page

2D and 3D reconstructions in acousto-electric tomography

We propose and test stable algorithms for the reconstruction of the internal conductivity of a biological object using acousto-electric measurements. Namely, the conventional impedance tomography scheme is supplemented by scanning the object with acoustic waves that slightly perturb the conductivity and cause the change in the electric potential measured on the boundary of the object. These perturbations of the potential are then used as the data for the reconstruction of the conductivity. The present method does not rely on "perfectly focused" acoustic beams. Instead, more realistic propagating spherical fronts are utilized, and then the measurements that would correspond to perfect focusing are synthesized. In other words, we use \emph{synthetic focusing}. Numerical experiments with simulated data show that our techniques produce high quality images, both in 2D and 3D, and that they remain accurate in the presence of high-level noise in the data. Local uniqueness and stability for the problem also hold

Time reversal in thermoacoustic tomography - an error estimate

The time reversal method in thermoacoustic tomography is used for approximating the initial pressure inside a biological object using measurements of the pressure wave made on a surface surrounding the object. This article presents error estimates for the time reversal method in the cases of variable, non-trapping sound speeds.Comment: 16 pages, 6 figures, expanded "Remarks and Conclusions" section, added one figure, added reference

Exact Site Percolation Thresholds Using the Site-to-Bond and Star-Triangle Transformations

I construct a two-dimensional lattice on which the inhomogeneous site percolation threshold is exactly calculable and use this result to find two more lattices on which the site thresholds can be determined. The primary lattice studied here, the ``martini lattice'', is a hexagonal lattice with every second site transformed into a triangle. The site threshold of this lattice is found to be $0.764826...$, while the others have $0.618034...$ and $1/\sqrt{2}$. This last solution suggests a possible approach to establishing the bound for the hexagonal site threshold, $p_c<1/\sqrt{2}$. To derive these results, I solve a correlated bond problem on the hexagonal lattice by use of the star-triangle transformation and then, by a particular choice of correlations, solve the site problem on the martini lattice.Comment: 12 pages, 10 figures. Submitted to Physical Review

An Evaluation of Protocols for UAV Science Applications

This paper identifies data transport needs for current and future science payloads deployed on the NASA Global Hawk Unmanned Aeronautical Vehicle (UAV). The NASA Global Hawk communication system and operational constrains are presented. The Genesis and Rapid Intensification Processes (GRIP) mission is used to provide the baseline communication requirements as a variety of payloads were utilized in this mission. User needs and desires are addressed. Protocols are matched to the payload needs and an evaluation of various techniques and tradeoffs are presented. Such techniques include utilization rate-base selective negative acknowledgement protocols and possible use of protocol enhancing proxies. Tradeoffs of communication architectures that address ease-of-use and security considerations are also presented

Reconstruction of a function from its spherical (circular) means with the centers lying on the surface of certain polygons and polyhedra

We present explicit filtration/backprojection-type formulae for the inversion of the spherical (circular) mean transform with the centers lying on the boundary of some polyhedra (or polygons, in 2D). The formulae are derived using the double layer potentials for the wave equation, for the domains with certain symmetries. The formulae are valid for a rectangle and certain triangles in 2D, and for a cuboid, certain right prisms and a certain pyramid in 3D. All the present inversion formulae yield exact reconstruction within the domain surrounded by the acquisition surface even in the presence of exterior sources.Comment: 9 figure

Uniqueness of reconstruction and an inversion procedure for thermoacoustic and photoacoustic tomography

The paper contains a simple approach to reconstruction in Thermoacoustic and Photoacoustic Tomography. The technique works for any geometry of point detectors placement and for variable sound speed satisfying a non-trapping condition. A uniqueness of reconstruction result is also obtained

Water movement into dormant and non-dormant wheat (Triticum aestivum L.) grains

The movement of water into harvest-ripe grains of dormant and non-dormant genotypes of wheat (Triticum aestivum L.) was investigated using Magnetic Resonance Micro-Imaging (MRMI). Images of virtual sections, both longitudinal and transverse, throughout the grain were collected at intervals after the start of imbibition and used to reconstruct a picture of water location within the different grain tissues and changes over time. The observations were supplemented by the weighing measurements of water content and imbibition of grains in water containing I2/KI which stains starch and lipid, thereby acting as a marker for water. In closely related genotypes, with either a dormant or a non-dormant phenotype, neither the rate of increase in water content nor the pattern of water distribution within the grain was significantly different until 18 h, when germination became apparent in the non-dormant genotype. Water entered the embryo and scutellum during the very early stages of imbibition through the micropyle and by 2 h water was clearly evident in the micropyle channel. After 12 h of imbibition, embryo structures such as the coleoptile and radicle were clearly distinguished. Although water accumulated between the inner (seed coat) and outer (pericarp) layers of the coat surrounding the grain, there was no evidence for movement of water directly across the coat and into the underlying starchy endosperm

Universality of finite-size corrections to the number of critical percolation clusters

Monte-Carlo simulations on a variety of 2d percolating systems at criticality suggest that the excess number of clusters in finite systems over the bulk value of nc is a universal quantity, dependent upon the system shape but independent of the lattice and percolation type. Values of nc are found to high accuracy, and for bond percolation confirm the theoretical predictions of Temperley and Lieb, and Baxter, Temperley, and Ashley, which we have evaluated explicitly in terms of simple algebraic numbers. Predictions for the fluctuations are also verified for the first time.Comment: 13 pages, 2 figs., Latex, submitted to Phys. Rev. Let