Quantitative Photo-acoustic Tomography with Partial Data

Photo-acoustic tomography is a newly developed hybrid imaging modality that combines a high-resolution modality with a high-contrast modality. We analyze the reconstruction of diffusion and absorption parameters in an elliptic equation and improve an earlier result of Bal and Uhlmann to the partial date case. We show that the reconstruction can be uniquely determined by the knowledge of 4 internal data based on well-chosen partial boundary conditions. Stability of this reconstruction is ensured if a convexity condition is satisfied. Similar stability result is obtained without this geometric constraint if 4n well-chosen partial boundary conditions are available, where $n$ is the spatial dimension. The set of well-chosen boundary measurements is characterized by some complex geometric optics (CGO) solutions vanishing on a part of the boundary.Comment: arXiv admin note: text overlap with arXiv:0910.250

Thermoacoustic tomography arising in brain imaging

We study the mathematical model of thermoacoustic and photoacoustic tomography when the sound speed has a jump across a smooth surface. This models the change of the sound speed in the skull when trying to image the human brain. We derive an explicit inversion formula in the form of a convergent Neumann series under the assumptions that all singularities from the support of the source reach the boundary

Metals from the ritual site of Shaitanskoye Ozero II (Sverdlovsk Oblast, Russia) [Metales del yacimiento ritual de Shaitanskoye Ozero II (provincia de Sverdlovsk Oblast, Rusia)]

The present article describes materials from the ritual site of Shaitanskoye Ozero II, Sverdlovsk Oblast. Few excavations carried out at the site measuring less than 240 sq. m in size, yielded more than 160 bronze artifacts: utensils, weapons, rolled copper ornaments, and abundant smelting and casting waste. Apart from Seima-Turbino (celts and laminar knives) and Eurasian types (daggers with cast hilts, truncated knives with guards, fluted bracelets and rings), several metal artifacts were revealed manufactured in the style of the Samus-Kizhirovo tradition. Bronze artifacts, stone knives and scrapers, and numerous arrowheads are accompanied by ceramics of the Koptyaki type. Metals use mainly a copper-tin alloy. This assemblage is shown to be relevant to the local tradition of metalworking, which, in this particular region, was comparatively ancient having been left uninterrupted by the rapid migrations of the Seima-Turbino people. In addition, the assemblage indicates the sources from which post-Seima artifacts reached the Alakul people. These artifacts may also have been linked with a large metalworking center located in the Middle Urals

Secure self-calibrating quantum random bit generator

Random bit generators (RBGs) are key components of a variety of information processing applications ranging from simulations to cryptography. In particular, cryptographic systems require "strong" RBGs that produce high-entropy bit sequences, but traditional software pseudo-RBGs have very low entropy content and therefore are relatively weak for cryptography. Hardware RBGs yield entropy from chaotic or quantum physical systems and therefore are expected to exhibit high entropy, but in current implementations their exact entropy content is unknown. Here we report a quantum random bit generator (QRBG) that harvests entropy by measuring single-photon and entangled two-photon polarization states. We introduce and implement a quantum tomographic method to measure a lower bound on the "min-entropy" of the system, and we employ this value to distill a truly random bit sequence. This approach is secure: even if an attacker takes control of the source of optical states, a secure random sequence can be distilled.Comment: 5 pages, 2 figure

Thermoacoustic tomography with variable sound speed

We study the mathematical model of thermoacoustic tomography in media with a variable speed for a fixed time interval, greater than the diameter of the domain. In case of measurements on the whole boundary, we give an explicit solution in terms of a Neumann series expansion. We give necessary and sufficient conditions for uniqueness and stability when the measurements are taken on a part of the boundary

Optical spectroscopy of Be stars: peak separation of Balmer emission lines

The Be stars display variable optical emission lines originating in the circumstellar disc. Here we analyse high resolution spectroscopic observations of Be stars and the distance between the peaks of H-alpha, H-beta, and H-gamma emission lines ($\Delta V_\alpha$, $\Delta V_\beta$, and $\Delta V_\gamma$ respectively). Combining published data, spectra from the ELODIE archive (obtained in the period 1998 -- 2003) and Rozhen spectra (obtained 2015 -- 2023) of 93 Be stars, we find a set of relations connecting $\Delta V_\alpha$, $\Delta V_\beta$ and $\Delta V_\gamma$. They are effective for $30 \le \Delta V_\alpha \le 500$ km s$^{-1}$, $80 \le \Delta V_\beta \le 600$ km s$^{-1}$, and $40 \le \Delta V_\gamma \le 300$ km s$^{-1}$. The new equations are in the form $y=ax + b$ and are valid for a wider velocity range than in previous studies.Comment: Astronomische Nachrichten (accepted

Inverse Diffusion Theory of Photoacoustics

This paper analyzes the reconstruction of diffusion and absorption parameters in an elliptic equation from knowledge of internal data. In the application of photo-acoustics, the internal data are the amount of thermal energy deposited by high frequency radiation propagating inside a domain of interest. These data are obtained by solving an inverse wave equation, which is well-studied in the literature. We show that knowledge of two internal data based on well-chosen boundary conditions uniquely determines two constitutive parameters in diffusion and Schroedinger equations. Stability of the reconstruction is guaranteed under additional geometric constraints of strict convexity. No geometric constraints are necessary when $2n$ internal data for well-chosen boundary conditions are available, where $n$ is spatial dimension. The set of well-chosen boundary conditions is characterized in terms of appropriate complex geometrical optics (CGO) solutions.Comment: 24 page

Stability of the gauge equivalent classes in stationary transport

For anisotropic attenuating media, the albedo operator determines the scattering and the attenuation coefficients up to a gauge transformation. We show that such a determination is stable

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