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

Oblivious RAM with O((log N)3) worst-case cost

LNCS v. 7073 entitled: Advances in Cryptology – ASIACRYPT 2011Oblivious RAM is a useful primitive that allows a client to hide its data access patterns from an untrusted server in storage outsourcing applications. Until recently, most prior works on Oblivious RAM aim to optimize its amortized cost, while suffering from linear or even higher worst-case cost. Such poor worst-case behavior renders these schemes impractical in realistic settings, since a data access request can occasionally be blocked waiting for an unreasonably large number of operations to complete. This paper proposes novel Oblivious RAM constructions that achieves poly-logarithmic worst-case cost, while consuming constant client-side storage. To achieve the desired worst-case asymptotic performance, we propose a novel technique in which we organize the O-RAM storage into a binary tree over data buckets, while moving data blocks obliviously along tree edges.postprin

On the spectral theory and dispersive estimates for a discrete Schrödinger equation in one dimension

This is the published version, also available here: http://dx.doi.org/10.1063/1.3005597.Based on the recent work [Komech et al., “Dispersive estimates for 1D discrete Schrödinger and Klein-Gordon equations,” Appl. Anal.85, 1487 (2006)] for compact potentials, we develop the spectral theory for the one-dimensional discrete Schrödinger operator, Hϕ=(−Δ+V)ϕ=−(ϕn+1+ϕn−1−2ϕn)+Vnϕn. We show that under appropriate decay conditions on the general potential (and a nonresonance condition at the spectral edges), the spectrum of H consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates ∥eitHPa.c.(H)∥l2σ→l2−σ≲t−3/2 for any fixed σ>52 and any t>0, where Pa.c.(H) denotes the spectral projection to the absolutely continuous spectrum of H. In addition, based on the scattering theory for the discrete Jost solutions and the previous results by Stefanov and Kevrekidis [“Asymptotic behaviour of small solutions for the discrete nonlinear Schrödinger and Klein-Gordon equations,” Nonlinearity18, 1841 (2005)], we find new dispersive estimates ∥eitHPa.c.(H)∥l1→l∞≲t−1/3, which are sharp for the discrete Schrödinger operators even for V=0

On the spectral theory and dispersive estimates for a discrete Schr\"{o}dinger equation in one dimension

Based on the recent work \cite{KKK} for compact potentials, we develop the spectral theory for the one-dimensional discrete Schr\"odinger operator H \phi = (-\De + V)\phi=-(\phi_{n+1} + \phi_{n-1} - 2 \phi_n) + V_n \phi_n. We show that under appropriate decay conditions on the general potential (and a non-resonance condition at the spectral edges), the spectrum of $H$ consists of finitely many eigenvalues of finite multiplicities and the essential (absolutely continuous) spectrum, while the resolvent satisfies the limiting absorption principle and the Puiseux expansions near the edges. These properties imply the dispersive estimates $$\|e^{i t H} P_{\rm a.c.}(H)\|_{l^2_{\sigma} \to l^2_{-\sigma}} \lesssim t^{-3/2}$$ for any fixed $\sigma > {5/2}$ and any $t > 0$, where $P_{\rm a.c.}(H)$ denotes the spectral projection to the absolutely continuous spectrum of $H$. In addition, based on the scattering theory for the discrete Jost solutions and the previous results in \cite{SK}, we find new dispersive estimates $$\|e^{i t H} P_{\rm a.c.}(H) \|_{l^1\to l^\infty}\lesssim t^{-1/3}.$$ These estimates are sharp for the discrete Schr\"{o}dinger operators even for $V = 0$

Asymptotic stability of small solitons in the discrete nonlinear Schrodinger equation in one dimension

Asymptotic stability of small solitons in one dimension is proved in the framework of a discrete nonlinear Schrodinger equation with septic and higher power-law nonlinearities and an external potential supporting a simple isolated eigenvalue. The analysis relies on the dispersive decay estimates from Pelinovsky & Stefanov (2008) and the arguments of Mizumachi (2008) for a continuous nonlinear Schrodinger equation in one dimension. Numerical simulations suggest that the actual decay rate of perturbations near the asymptotically stable solitons is higher than the one used in the analysis.Comment: 21 pages, 2 figure

Scalar-tensor black holes coupled to Born-Infeld nonlinear electrodynamics

The non-existence of asymptotically flat, neutral black holes and asymptotically flat, charged black holes in the Maxwell electrodynamics, with non-trivial scalar field has been proved for a large class of scalar-tensor theories. The no-scalar-hair theorems, however, do not apply in the case of non-linear electrodynamics. In the present work numerical solutions describing charged black holes coupled to Born-Infeld type non-linear electrodynamics in scalar-tensor theories of gravity with massless scalar field are found. The causal structure and properties of the solutions are studied, and a comparison between these solutions and the corresponding solutions in the General Relativity is made. The presence of the scalar field leads to a much more simple causal structure. The present class of black holes has a single, non-degenerate horizon, i.e., its causal structure resembles that of the Schwarzschild black hole.Comment: 12 pages, 4 figures, PR

Direct Energy Production From Hydrogen Sulfide in Black Sea Water - Electrochemical Study

A sulfide driven fuel cell is proposed to clean the Black Sea with the simultaneous A sulfide driven fuel cell is proposed to clean the Black Sea with the simultaneous production of energy. The process is hopeful even at low sulfide concentrations, i.e.10 to 25 mg/l being close to the ones in the Black Sea water. The main problem for the practical application of this type of fuel cell are the low current and power densities. The measurement of the generated electric current compared to the sulfide depletion show that the most probable anode reaction is oxidation of sulfide to sulfate. It is evident that parasite competitive reactions oxidation of sulfide occurs in the anode compartment of the fuel cell. The pH measurements shows that the transfer of hydroxylic anions from the cathodic compartment to the anodic one across the separating membrane is not fast enough to compensate its drop in the anode compartment

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

Nonlinearity Management in Higher Dimensions

In the present short communication, we revisit nonlinearity management of the time-periodic nonlinear Schrodinger equation and the related averaging procedure. We prove that the averaged nonlinear Schrodinger equation does not support the blow-up of solutions in higher dimensions, independently of the strength in the nonlinearity coefficient variance. This conclusion agrees with earlier works in the case of strong nonlinearity management but contradicts those in the case of weak nonlinearity management. The apparent discrepancy is explained by the divergence of the averaging procedure in the limit of weak nonlinearity management.Comment: 9 pages, 1 figure