Symbolic Knowledge Extraction from Trained Neural Networks Governed by Lukasiewicz Logics

This work describes a methodology to extract symbolic rules from trained neural networks. In our approach, patterns on the network are codified using formulas on a Lukasiewicz logic. For this we take advantage of the fact that every connective in this multi-valued logic can be evaluated by a neuron in an artificial network having, by activation function the identity truncated to zero and one. This fact simplifies symbolic rule extraction and allows the easy injection of formulas into a network architecture. We trained this type of neural network using a back-propagation algorithm based on Levenderg-Marquardt algorithm, where in each learning iteration, we restricted the knowledge dissemination in the network structure. This makes the descriptive power of produced neural networks similar to the descriptive power of Lukasiewicz logic language, minimizing the information loss on the translation between connectionist and symbolic structures. To avoid redundance on the generated network, the method simplifies them in a pruning phase, using the "Optimal Brain Surgeon" algorithm. We tested this method on the task of finding the formula used on the generation of a given truth table. For real data tests, we selected the Mushrooms data set, available on the UCI Machine Learning Repository.

Study of the one dimensional and transient bioheat transfer equation: Multi-layer solution development and applications

: In this work we derive an analytical solution given by Bessel series to the transient and one-dimensional (1D) bioheat transfer equation in a multi-layer region with spatially dependent heat sources. Each region represents an independent biological tissue characterized by temperature-invariant physiological parameters and a linearly temperature dependent metabolic heat generation. Moreover, 1D Cartesian, cylindrical or spherical coordinates are used to define the geometry and temperature boundary conditions of first, second and third kinds are assumed at the inner and outer surfaces. We present two examples of clinical applications for the developed solution. In the first one, we investigate two different heat source terms to simulate the heating in a tumor and its surrounding tissue, induced during a magnetic fluid hyperthermia technique used for cancer treatment. To obtain an accurate analytical solution, we determine the error associated with the truncated Bessel series that defines the transient solution. In the second application, we explore the potential of this model to study the effect of different environmental conditions in a multi-layered human head model (brain, bone and scalp). The convective heat transfer effect of a large blood vessel located inside the brain is also investigated. The results are further compared with a numerical solution obtained by the Finite Element Method and computed with COMSOL Multi-physics v4.1 (c). (c) 2013 Elsevier Ltd. All rights reserved.

Citologia da cúpula vaginal com suspeita de lesão intraepitelial de grau indeterminado: estudo de caso

No presente artigo é relatado um caso de uma paciente de 42 anos, diagnosticada em 2011 com Adenocarcinoma in situ e displasia grave do epitélio de revestimento pavimentoso, que foi tratada por traquelectomia. Em Novembro de 2013, a paciente realizou uma citologia da cúpula vaginal, onde se observaram achados citológicos compatíveis com lesão intraepitelial de baixo grau mas também a presença de células que favorecem o diagnóstico de lesão intraepitelial de alto grau. Não sendo possível classificar a lesão intraepitelial como sendo claramente baixo ou alto grau, atribuiu-se a interpretação de lesão intraepitelial de grau indeterminado. Para confirmação e esclarecimento do diagnóstico foi efetuada biopsia com resultado de displasia grave do epitélio de revestimento pavimentoso vaginal sem evidência de invasão do estroma. Por fim foi indicada a pesquisa e tipificação de vírus do papiloma humano, com resultado positivo para o tipo 16. Diagnósticos citológicos de lesão intraepitelial de grau indeterminado apresentam um follow-up histológico estatisticamente diferente das lesões intraepiteliais de alto e baixo grau, e estão na sua maioria associadas a infeção por vírus do papiloma humano de alto risco. Os achados citológicos do presente estudo apoiam a necessidade de se estabelecer esta lesão como categoria de diagnóstico no Sistema de Bethesda, com um follow-up definido.