Pareto optimality conditions and duality for vector quadratic fractional optimization problems

One of the most important optimality conditions to aid in solving a vector optimization problem is the first-order necessary optimality condition that generalizes the Karush-Kuhn-Tucker condition. However, to obtain the sufficient optimality conditions, it is necessary to impose additional assumptions on the objective functions and on the constraint set. The present work is concerned with the constrained vector quadratic fractional optimization problem. It shows that sufficient Pareto optimality conditions and the main duality theorems can be established without the assumption of generalized convexity in the objective functions, by considering some assumptions on a linear combination of Hessian matrices instead. The main aspect of this contribution is the development of Pareto optimality conditions based on a similar second-order sufficient condition for problems with convex constraints, without convexity assumptions on the objective functions. These conditions might be useful to determine termination criteria in the development of algorithms.Coordenação de aperfeiçoamento de pessoal de nivel superior (Brasil)Ministerio de Ciencia y TecnologíaConselho Nacional de Desenvolvimento Científico e Tecnológico (Brasil)Fundação de Amparo à Pesquisa do Estado de São Paul

Direito Registral Imobiliário

Divulgação dos SUMÁRIOS das obras recentemente incorporadas ao acervo da Biblioteca Ministro Oscar Saraiva do STJ. Em respeito à lei de Direitos Autorais, não disponibilizamos a obra na íntegra. Localização: 347.235(81) S168d Código de barras: STJ00063785Trata-se de obra que busca suprir a necessidade de trabalhos doutrinários envolvendo o segmento do Direito Registral Imobiliário, e traz inovações e questionamentos necessários para o debate envolvendo o "direito de propriedade" e as formas que o alicerçam. Ressalta a significativa importância das ações de retificação e nulidade de registro após o advento da Lei n. 10.931, de 4 de agosto de 2004, desvendando os pontos que estruturam esses procedimentos. Enfoca com profundidade a questão da segurança jurídica no Direito Registral Imobiliário, bem destacando que esta, em absoluto, repousa na perpetuidade das formas e dos registros

Scalability of GHZ and random-state entanglement in the presence of decoherence

We derive analytical upper bounds for the entanglement of generalized Greenberger-Horne-Zeilinger states coupled to locally depolarizing and dephasing environments, and for local thermal baths of arbitrary temperature. These bounds apply for any convex quantifier of entanglement, and exponential entanglement decay with the number of constituent particles is found. The bounds are tight for depolarizing and dephasing channels. We also show that randomly generated initial states tend to violate these bounds, and that this discrepancy grows with the number of particles.Comment: 9 pages, 3 figure

A role of diffusion tensor imaging in movement disorder surgery

The safe and reversible nature of deep brain stimulation (DBS) has allowed movement disorder neurosurgery to become commonplace throughout the world. Fundamental understanding of individual patient’s anatomy is critical for optimizing the effects and side effects of DBS surgery. Three patients undergoing stereotactic surgery for movement disorders, at the institution’s intraoperative magnetic resonance imaging operating suite, were studied with fiber tractography. Stereotactic targets and fiber tractography were determined on preoperative magnetic resonance imagings using the Schaltenbrand–Wahren atlas for definition in the BrainLab iPlan software (BrainLAB Inc., Feldkirchen, Germany). Subthalamic nucleus, globus pallidus interna, and ventral intermediate nucleus targets were studied. Diffusion tensor imaging parameters used ranged from 2 to 8 mm for volume of interest in the x/y/z planes, fiber length was kept constant at 30 mm, and fractional anisotropy threshold varied from 0.20 to 0.45. Diffusion tensor imaging tractography allowed reliable and reproducible visualization and correlation between frontal eye field, premotor, primary motor, and primary sensory cortices via corticospinal tracts and corticopontocerebellar tracts. There is an apparent increase in the number of cortical regions targeted by the fiber tracts as the region of interest is enlarged. This represents a possible mechanism of the increased effects and side effects observed with higher stimulation voltages. Currently available diffusion tensor imaging techniques allow potential methods to characterize the effects and side effects of DBS. This technology has the potential of being a powerful tool to optimize DBS neurosurgery

Nonlinear cutting stock problem model to minimize the number of different patterns and objects

In this article we solve a nonlinear cutting stock problem which represents a cutting stock problem that considers the minimization of, both, the number of objects used and setup. We use a linearization of the nonlinear objective function to make possible the generation of good columns with the Gilmore and Gomory procedure. Each time a new column is added to the problem, we solve the original nonlinear problem by an Augmented Lagrangian method. This process is repeated until no more profitable columns is generated by Gilmore and Gomory technique. Finally, we apply a simple heuristic to obtain an integral solution for the original nonlinear integer problem.617

Gamma knife radiosurgery for vestibular schwannomas: evaluation of planning using the sphericity degree of the target volume

This study explores the possibility of a relationship between the sphericity degree of a target volume with the dose distribution. This relationship is evaluated based on the ratio isodose volume / target volume (IV/TV) and the metrics coverage, i.e., selectivity, gradient index, conformity index and mean dose when planning radiosurgery for vestibular schwannoma. Methods: Sphericity degree (φ) was calculated for each target volume (TV) of 64 patients who underwent stereotactic radiosurgery (SRS) for vestibular schwannoma. The calculation of this parameter was developed using the theoretical definition for operational sphericity φ = VP/VCS. The values found are evaluated considering the following metrics:-Coverage (C), selectivity (S), gradient index (GI), Paddick conformity index (CIPaddick) and dose distribution (IV/TV). The planning was also carried out considering a spherical target volume defined in a spherical phantom. The spherical volume is the same as the target used in the treatment plan. The planning of the spherical target was considered as a reference plan to evaluate the dose distribution inside and outside the volume. Results: It was possible to observe that the majority of target volumes has (.) around 0,66.0,77, corresponding to 54,7% of the total. Considering the mean values for metrics, the results are: C = 0,98, S = 0,78, GI = 3,11 and CI = 0,81. The dose distribution was equivalent for treatment plans and reference plans. Quantitative analysis for IV/TV shows that these values are higher than 30% for treatment plans where shot density is large. Conclusion: This study demonstrates that de sphericity degree (φ) can be related to the dose distribution (IV/TV). Therefore the sphericity degree is a good parameter to evaluate the dose distribution of a plan for vestibular schwannoma treatment, considering the reference plan as being a spherical target using a leksell gamma knife® perfexion (LGKP). This study shows that the sphericity degree offers important information of the dose distribution outside and inside the target volume. This is not evaluated by the other parameters already implemented as metric to analyzing the GKP plans15