Adaptive field-of-view imaging for efficient receive beamforming in medical ultrasound imaging systems

Quadrature demodulation-based phase rotation beamforming (QD-PRBF) is commonly used to support dynamic receive focusing in medical ultrasound systems. However, it is computationally demanding since it requires two demodulation filters for each receive channel. To reduce the computational requirements of QD-PRBF, we have previously developed two-stage demodulation (TSD), which reduces the number of lowpass filters by performing demodulation filtering on summation signals. However, it suffers from image quality degradation due to aliasing at lower beamforming frequencies. To improve the performance of TSD-PRBF with reduced number of beamforming points, we propose a new adaptive field-of-view (AFOV) imaging method. In AFOV imaging, the beamforming frequency is adjusted depending on displayed FOV size and the center frequency of received signals. To study its impact on image quality, simulation was conducted using Field II, phantom data were acquired from a commercial ultrasound machine, and the image quality was quantified using spatial (i.e., axial and lateral) and contrast resolution. The developed beamformer (i.e., TSD-AFOV-PRBF) with 1024 beamforming points provided comparable image resolution to QD-PRBF for typical FOV sizes (e.g., 4.6% and 1.3% degradation in contrast resolution for 160 mm and 112 mm, respectively for a 3.5 MHz transducer). Furthermore, it reduced the number of operations by 86.8% compared to QD-PRBF. These results indicate that the developed TSD-AFOV-PRBF can lower the computational requirement for receive beamforming without significant image quality degradation.     

On absence of diffusion near the bottom of the spectrum for a random Schrödinger operator onL 2(ℝ)+

We consider a random Schrödinger operator onL ²(^v) of the form , {C _i} being a covering of ^v with unit cubes around the sites of ^v and {q _i} i.i.d. random variables with values in [0, 1]. We assume that theq _i's are continuously distributed with bounded densityf(q) and that 0<P(q ₀<1/2)=<1. Then we show that an ergodic mean of the quantity dx|x|²|(exp(itH ))(x)|²t ^–1 vanishes provided =g _E(H ), where is well-localized around the origin andg _E is a positiveC -function with support in (0,E),EE*(, |f|). Our estimate ofE*(, |f|) is such that the set {x ^v |V (x) E*(, |f|)} may contain with probability one an infinite cluster of cubes {C _i} which are nearest neighbours. The proof is based on the technique introduced by Fröhlich and Spencer for the analysis of the Anderson model.Work supported in part by C.N.R. (Italy) and NAVF (Norway)On leave of absence from Instituto di Fisica Università di Roma, Italia     

Permanence and Positive Periodic Solutions for Kolmogorov Competing Species Systems

We prove the existence of periodic solutions in a compact attractor of (R⁺)ⁿ for the Kolmogorov system x′_i = x_if_i(t, x₁, …, x_n), i = l, …, n in the competitive case. Extension to differential delay equations are con- sidered too. Applications are given to Lotka-Volterra systems with periodic coefficients.     

Boundary blow-up for differential equations with indefinite weight

We obtain results of existence and multiplicity of solutions for the second-order equation x″+q(t)g(x)=0, with x(t) defined for all t∈]0,1[ and such that x(t)→+∞ as t→0⁺ and t→1⁻. We assume g having superlinear growth at infinity and q(t) possibly changing sign on [0,1].     

On some recent proposals for testing macrorealism versus quantum mechanics

In order to evaluate its relevance, we reconsider critically the recent proposal by Leggett and Garg to test macrorealism against quantum mechanics by resorting to experiments involving noninvasive measurement processes on a SQUID. Our conclusion is that, in spite of the fact that the proposed experiment would neither constitute a test of macrorealism nor a test of macrocontextuality, a simplified form of it represents a (presumably) feasible experiment permitting a direct test of macroscopic quantum coherence. We also analyze the proposal from the point of view of the recent attempts to build up model theories allowing to take, within a purely quantum framework, a macrorealistic position about natural phenomena, i.e., the socalled dynamical reduction models and we stress that the proposed experiment has no relevance for the dynamical reduction program, as developed so far. However consideration of the SQUID system allows one to test other possible dynamical mechanisms leading to the objectification of macroproperties which could, in principle, be operative. We also briefly sketch experimental procedures to be followed to get all relevant information concerning macrocoherence.     

On a new stochastic global optimization algorithm based on censored observations

In this paper a new algorithm is proposed for global optimization problems. The main idea is that of modifying a standard clustering approach by sequentially sampling the objective function while adaptively deciding an appropriate sample size. Theoretical as well as computational results are presented.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

Sequential stopping rules for the multistart algorithm in global optimisation

In this paper a sequential stopping rule is developed for the Multistart algorithm. A statistical model for the values of the observed local maxima of an objective function is introduced in the framework of Bayesian non-parametric statistics. A suitablea-priori distribution is proposed which is general enough and which leads to computationally manageable expressions for thea-posteriori distribution. Sequential stopping rules of thek-step look-ahead kind are then explicitly derived, and their numerical effectiveness compared.     

Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.