Numerical approximation of incompressible flows with net flux defective boundary conditions by means of penalty techniques

We consider incompressible flow problems with defective boundary conditions prescribing only the net flux on some inflow and outflow sections of the boundary. As a paradigm for such problems, we simply refer to Stokes flow. After a brief review of the problem and of its well posedness, we discretize the corresponding variational formulation by means of finite elements and looking at the boundary conditions as constraints, we exploit a penalty method to account for them. We perform the analysis of the method in terms of consistency, boundedness and stability of the discrete bilinear form and we show that the application of the penalty method does not affect the optimal convergence properties of the finite element discretization. Since the additional terms introduced to account for the defective boundary conditions are non-local, we also analyze the spectral properties of the equivalent algebraic formulation and we exploit the analysis to set up an efficient solution strategy. In contrast to alternative discretization methods based on Lagrange multipliers accounting for the constraints on the boundary, the present scheme is particularly effective because it only mildly affects the structure and the computational cost of the numerical approximation. Indeed, it does not require neither multipliers nor sub-iterations or additional adjoint problems with respect to the reference problem at hand.     

A Brief Critique of Pure Hypercomputation

Hypercomputation—the hypothesis that Turing-incomputable objects can be computed through infinitary means—is ineffective, as the unsolvability of the halting problem for Turing machines depends just on the absence of a definite value for some paradoxical construction; nature and quantity of computing resources are immaterial. The assumption that the halting problem is solved by oracles of higher Turing degree amounts just to postulation; infinite-time oracles are not actually solving paradoxes, but simply assigning them conventional values. Special values for non-terminating processes are likewise irrelevant, since diagonalization can cover any amount of value assignments. This should not be construed as a restriction of computing power: Turing’s uncomputability is not a ‘barrier’ to be broken, but simply an effect of the expressive power of consistent programming systems.     

Decentralized multi-robot encirclement of a 3D target with guaranteed collision avoidance

We present a control framework for achieving encirclement of a target moving in 3D using a multi-robot system. Three variations of a basic control strategy are proposed for different versions of the encirclement problem, and their effectiveness is formally established. An extension ensuring maintenance of a safe inter-robot distance is also discussed. The proposed framework is fully decentralized and only requires local communication among robots; in particular, each robot locally estimates all the relevant global quantities. We validate the proposed strategy through simulations on kinematic point robots and quadrotor UAVs, as well as experiments on differential-drive wheeled mobile robots.     

A Note on the Equivalence of Coherence and Constrained Coherence

Constrained coherence is compared to coherence and its role in the behavioural interpretation of coherence is discussed. The equivalence of these two notions is proven for coherent conditional previsions, showing that the same course of reasoning applies to several similar concepts developed in the realm of imprecise probability theory.     

An innovative <Emphasis Type="BoldItalic">H</Emphasis><Subscript><Emphasis Type="BoldItalic">∞</Emphasis></Subscript>–norm based worst case scenario approach for dynamic compliance optimization with applications to viscoelastic beams

A novel frequency–based definition of dynamic compliance is introduced within the framework of H _∞ –norm based structural dynamics in the presence of load uncertainties. The system itself is supposed to depend on a vector of design parameters with respect to which an optimal design is pursued. A three-step worst-case-scenario is then developed that finds the minimum-compliance structure capable of accounting for the entire norm–bounded load sets. Once the problem is initialized, the current worst load is found that is used as input to the minimization of the structural compliance and the procedure is repeated until convergence. Numerical examples are eventually proposed that deal with viscoelastic beams discretized via a truly–mixed finite–element scheme.     

Time-relevant stability of 2D systems

For many 2D systems, one of the independent variables plays a distinct role in the evolution of the trajectories; since often this special independent variable is time, we call such systems ‘time-relevant’. In this paper, we introduce a stability notion for time-relevant systems described by higher-order difference equations. We give algebraic tests in terms of the location of the zeros of the determinant of a polynomial matrix describing the system. We also give an LMI characterization of time-relevant stability involving only constant matrices.     

Interactive visual analysis of contrast-enhanced ultrasound data based on small neighborhood statistics

Contrast-enhanced ultrasound (CEUS) has recently become an important technology for lesion detection and characterization in cancer diagnosis. CEUS is used to investigate the perfusion kinetics in tissue over time, which relates to tissue vascularization. In this paper we present a pipeline that enables interactive visual exploration and semi-automatic segmentation and classification of CEUS data.For the visual analysis of this challenging data, with characteristic noise patterns and residual movements, we propose a robust method to derive expressive enhancement measures from small spatio-temporal neighborhoods. We use this information in a staged visual analysis pipeline that leads from a more local investigation to global results such as the delineation of anatomic regions according to their perfusion properties. To make the visual exploration interactive, we have developed an accelerated framework based on the OpenCL library, that exploits modern many-cores hardware. Using our application, we were able to analyze datasets from CEUS liver examinations, being able to identify several focal liver lesions, segment and analyze them quickly and precisely, and eventually characterize them.     

Objective quantification of acetylcholine receptor aggregation using fast Fourier transforms

A new approach for objectively analyzing the aggregation of acetylcholine receptors (AChRs) through power spectrum analysis derived from fast Fourier transform (FFT) of images has been developed. Presently, detection of AChR aggregates at neuromuscular junctions is not easily accomplished. Though the formation of AChR clusters results in periodic gray-level variations that differ with time, no study reporting their correlation with frequency information in the Fourier domain for aggregates' detection purposes exists. To this end, we processed time-lapse images of AChR aggregates' formation on murine myotubes to extract peak values of power spectra. To validate interpretation of the Fourier spectra analysis, a computer routine was developed to semi-automatically count AChR aggregates. We found: (1) logarithmic maxima of Fourier spectra correlated significantly with experimentation time; (2) cluster count correlated significantly with time only after clusters were discernable from images, signifying that this method heavily depended on definitive growth data and thresholding values; (3) exponents of Fourier maxima versus time and cluster count versus time profiles during this phase compared favorably, indicating that both methods were analyzing identical cluster growth rates. Our observations suggest that analysis via FFT power spectrum is sensitive and robust enough to automatically quantify AChR aggregates.