Cramer-Rao Lower Bound for Point Based Image Registration with Heteroscedastic Error Model for Application in Single Molecule Microscopy

The Cramer-Rao lower bound for the estimation of the affine transformation parameters in a multivariate heteroscedastic errors-in-variables model is derived. The model is suitable for feature-based image registration in which both sets of control points are localized with errors whose covariance matrices vary from point to point. With focus given to the registration of fluorescence microscopy images, the Cramer-Rao lower bound for the estimation of a feature's position (e.g. of a single molecule) in a registered image is also derived. In the particular case where all covariance matrices for the localization errors are scalar multiples of a common positive definite matrix (e.g. the identity matrix), as can be assumed in fluorescence microscopy, then simplified expressions for the Cramer-Rao lower bound are given. Under certain simplifying assumptions these expressions are shown to match asymptotic distributions for a previously presented set of estimators. Theoretical results are verified with simulations and experimental data

Quantal Brownian Motion - Dephasing and Dissipation

We analyze quantal Brownian motion in $d$ dimensions using the unified model for diffusion localization and dissipation, and Feynman-Vernon formalism. At high temperatures the propagator possess a Markovian property and we can write down an equivalent Master equation. Unlike the case of the Zwanzig-Caldeira-Leggett model, genuine quantum mechanical effects manifest themselves due to the disordered nature of the environment. Using Wigner picture of the dynamics we distinguish between two different mechanisms for destruction of coherence. The analysis of dephasing is extended to the low temperature regime by using a semiclassical strategy. Various results are derived for ballistic, chaotic, diffusive, both ergodic and non-ergodic motion. We also analyze loss of coherence at the limit of zero temperature and clarify the limitations of the semiclassical approach. The condition for having coherent effect due to scattering by low-frequency fluctuations is also pointed out. It is interesting that the dephasing rate can be either larger or smaller than the dissipation rate, depending on the physical circumstances.Comment: LaTex, 23 pages, 4 figures, published vesio

Energy diffusion in frustrated quantum spin chains exhibiting Gaussian orthogonal ensemble level statistics

Frustrated quantum $XXZ$ spin chains with the next-nearest-neighbor (NNN) couplings are typically deterministic many-body systems exhibiting Gaussian orthogonal ensemble (GOE) spectral statistics. We investigate energy diffusion for these spin chains in the presence of a periodically oscillating magnetic field. Diffusion coefficients are found to obey the power law with respect to both the field strength and driving frequency with its power varying depending on the linear response and non-perturbative regimes. The widths of the linear response and the non-perturbative regimes depend on the strength of frustrations. We have also elucidated a mechanism for oscillation of energy diffusion in the case of weakened frustrations.Comment: 6 pages, 6 figure

Deconfinement in the Quark Meson Coupling Model

The Quark Meson Coupling Model which describes nuclear matter as a collection of non-overlapping MIT bags interacting by the self-consistent exchange of scalar and vector mesons is used to study nuclear matter at finite temperature. In its modified version, the density dependence of the bag constant is introduced by a direct coupling between the bag constant and the scalar mean field. In the present work, the coupling of the scalar mean field with the constituent quarks is considered exactly through the solution of the Dirac equation. Our results show that a phase transition takes place at a critical temperature around 200 MeV in which the scalar mean field takes a nonzero value at zero baryon density. Furthermore it is found that the bag constant decreases significantly when the temperature increases above this critical temperature indicating the onset of quark deconfinement.Comment: LaTeX/TeX 15 pages (zk2.tex)+ 6 figures in TeX forma

Pressure-Induced Anomalous Phase Transitions and Colossal Enhancement of Piezoelectricity in PbTiO3_3

We find an unexpected tetragonal-to-monoclinic-to-rhombohedral-to-cubic phase transition sequence induced by pressure, and a morphotropic phase boundary in a pure compound using first-principles calculations. Huge dielectric and piezoelectric coupling constants occur in the transition regions, comparable to those observed in the new complex single-crystal solid-solution piezoelectrics such as Pb(Mg$_{1/3}$Nb$_{2/3}$)O$_{3}$-PbTiO$_{3}$, which are expected to revolutionize electromechanical applications. Our results show that morphotropic phase boundaries and giant piezoelectric effects do not require intrinsic disorder, and open the possibility of studying this effect in simple systems.Comment: 4 pages, to appear in Phys. Rev. Let

Investigation of Quantum Chaos in the Parametric Dependent System of Interacting oscillators

Formation of chaos in the parametric dependent system of interacting oscillators for the both classical and quantum cases has been investigated. Domain in which classical motion is chaotic is defined. It has been shown that for certain values of the parameters from this domain, form of the classical power spectrum is in a good agreement with the quantum band profile. Local density of states is calculated. The range in which application of perturbation theory is correct has been defined.Comment: 9 figures. to be published in Mod.Phys.Lett.

Mapping the dynamic interactions between vortex species in highly anisotropic superconductors

Here we use highly sensitive magnetisation measurements performed using a Hall probe sensor on single crystals of highly anisotropic high temperature superconductors $Bi_{2}Sr_{2}CaCu_{2}O_{8}$ to study the dynamic interactions between the two species of vortices that exist in such superconductors. We observe a remarkable and clearly delineated high temperature regime that mirrors the underlying vortex phase diagram. Our results map out the parameter space over which these dynamic interaction processes can be used to create vortex ratchets, pumps and other fluxonic devices.Comment: 7 pages, 3 figures, to be published in Supercond. Sci. Techno

Re-exploration of vertical rectus abdominis myocutaneous flap for vaginal reconstruction: Case report and review of the literature.

The vertical rectus abdominis myocutaneous (VRAM) flap is a versatile and well-established reconstructive technique for many defects created as a result of colorectal and gynecologic extirpation. However, major re-operation in the pelvis following a VRAM flap reconstruction several months later is uncommon, and the safety and integrity of the VRAM flap in this setting has not been described. This case examines VRAM flap preservation during repeat exploratory laparotomy, and a unique view of the VRAM flap during interval exploration. We demonstrate an intact flap after lysis of adhesions with an audible Doppler signal, and maintenance of flap integrity in the postoperative period. This further substantiates its use as a durable rotational flap for perineal tissue defects