The final publication is available at link.springer.com. An Optimal Control Approach to Find Sparse Data for Laplace Interpolation

Abstract. Finding optimal data for inpainting is a key problem in the context of partial differential equation-based image compression. We present a new model for optimising the data used for the reconstruction by the underlying homogeneous diffusion process. Our approach is based on an optimal control framework with a strictly convex cost functional containing an L1 term to enforce sparsity of the data and non-convex constraints. We propose a numerical approach that solves a series of convex optimisation problems with linear constraints. Our numerical examples show that it outperforms existing methods with respect to quality and computation time

Microscope and microâ camera assessment of Schneiderian membrane perforation via transcrestal sinus floor elevation: A randomized ex vivo study

ObjectiveWe sought to assess the effectiveness of using a microscope and nonâ invasive camera for assessing sinus membrane perforations during transcrestal sinus floor elevation (TSFE).Materials and methodsFive fresh human cadaver heads corresponding to eight maxillary sinuses (six bilateral and two unilateral) underwent 4 TSFEs per sinus (a total of 32 single site elevations). Each elevation was randomly assigned to receive a three or six mm membrane elevation height (MEH). A microscope and microâ camera were used to assess the sinus membrane perforation. Afterwards, radiological and clinical membrane perforation assessments were performed. The statistical analysis results are expressed using the means, standard deviations, range values of the residual ridge height (RRH), residual ridge width (RRW), sinus membrane thickness (SMT) and incidence of perforation (IoP). Generalized linear methods were used to test for the correlation of RRH and MEH to the microscope and microâ camera perforation assessments and the correlation of microscope and microâ camera assessments with the postâ operative CBCT and crestal liquid evaluation.ResultsThe cumulative percentage of IoP was 40.62%, (23.07% with 3 mm MEH, and 76.92% with 6 mm MEH, p < 0.05). The perforation assessed using either the microscope or microâ camera coincided with the postâ operative CBCT and crestal liquid assessment in 87.55% sites. No significant correlation was found between the microscope or microâ camera assessments with RRH or MEH.ConclusionApplication of a microscope and microâ camera during transcrestal sinus floor elevation may allow the detection of the integrity of the Schneiderian membrane with greater than 85% accuracy in this ex vivo model.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149727/1/clr13453.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149727/2/clr13453_am.pd

A combined first and second order variational approach for image reconstruction

In this paper we study a variational problem in the space of functions of bounded Hessian. Our model constitutes a straightforward higher-order extension of the well known ROF functional (total variation minimisation) to which we add a non-smooth second order regulariser. It combines convex functions of the total variation and the total variation of the first derivatives. In what follows, we prove existence and uniqueness of minimisers of the combined model and present the numerical solution of the corresponding discretised problem by employing the split Bregman method. The paper is furnished with applications of our model to image denoising, deblurring as well as image inpainting. The obtained numerical results are compared with results obtained from total generalised variation (TGV), infimal convolution and Euler's elastica, three other state of the art higher-order models. The numerical discussion confirms that the proposed higher-order model competes with models of its kind in avoiding the creation of undesirable artifacts and blocky-like structures in the reconstructed images -- a known disadvantage of the ROF model -- while being simple and efficiently numerically solvable.Comment: 34 pages, 89 figure

Refining Inductive Types

Dependently typed programming languages allow sophisticated properties of data to be expressed within the type system. Of particular use in dependently typed programming are indexed types that refine data by computationally useful information. For example, the N-indexed type of vectors refines lists by their lengths. Other data types may be refined in similar ways, but programmers must produce purpose-specific refinements on an ad hoc basis, developers must anticipate which refinements to include in libraries, and implementations must often store redundant information about data and their refinements. In this paper we show how to generically derive inductive characterisations of refinements of inductive types, and argue that these characterisations can alleviate some of the aforementioned difficulties associated with ad hoc refinements. Our characterisations also ensure that standard techniques for programming with and reasoning about inductive types are applicable to refinements, and that refinements can themselves be further refined

Dinâmica do uso e cobertura do solo em áreas queimadas de municípios na Amazônia brasileira.

The disordered occupation in the Amazon, the population growth due the National Integration Plan and the lack of new techniques and technologies diffusion for crops management, economically accessible and less aggressiveness to the environment, resulted in the suppression of the natural forest in approximately 25% of the total area Of the Amazon. A factor associated with this suppression, due to its economic viability and local culture, the fire, is used for the conversion of forests to agricultural areas and the maintenance of previously established crops. In order to study this context, the present paper had as objective to identify the classes of land use and cover associated with the fire spots detected by satellites, also indicating burn recurrence areas for the municipalities of Santa Maria das Barreiras - PA, Colniza-MT And Porto Velho - RO.The results indicate that in the period from 2008 to 2014, 67% of the areas associated with the fire spots presented "Low" occurrence, associated mainly with the "Pasture" classes. There was an average loss of forest area of 7.2% over low recurrence areas, while in high recurrence areas there was an average loss of 22.5

LHC and lepton flavour violation phenomenology of a left-right extension of the MSSM

We study the phenomenology of a supersymmetric left-right model, assuming minimal supergravity boundary conditions. Both left-right and (B-L) symmetries are broken at an energy scale close to, but significantly below the GUT scale. Neutrino data is explained via a seesaw mechanism. We calculate the RGEs for superpotential and soft parameters complete at 2-loop order. At low energies lepton flavour violation (LFV) and small, but potentially measurable mass splittings in the charged scalar lepton sector appear, due to the RGE running. Different from the supersymmetric 'pure seesaw' models, both, LFV and slepton mass splittings, occur not only in the left- but also in the right slepton sector. Especially, ratios of LFV slepton decays, such as Br(${\tilde\tau}_R \to \mu \chi^0_1$)/Br(${\tilde\tau}_L \to \mu \chi^0_1$) are sensitive to the ratio of (B-L) and left-right symmetry breaking scales. Also the model predicts a polarization asymmetry of the outgoing positrons in the decay $\mu^+ \to e^+ \gamma$, A ~ [0,1], which differs from the pure seesaw 'prediction' A=1$. Observation of any of these signals allows to distinguish this model from any of the three standard, pure (mSugra) seesaw setups.Comment: 43 pages, 17 figure