980 research outputs found
Sobriety of crisp and fuzzy topological spaces
The objective of this thesis is a survey of crisp and fuzzy sober topological spaces. We begin by examining sobriety of crisp topological spaces. We then extend this to the L- topological case and obtain analogous results and characterizations to those of the crisp case. We then brie y examine semi-sobriety of (L;M)-topological spaces
Sobriety of crisp and fuzzy topological spaces
The objective of this thesis is a survey of crisp and fuzzy sober topological spaces. We begin by examining sobriety of crisp topological spaces. We then extend this to the L- topological case and obtain analogous results and characterizations to those of the crisp case. We then brie y examine semi-sobriety of (L;M)-topological spaces
A Recipe for State-and-Effect Triangles
In the semantics of programming languages one can view programs as state
transformers, or as predicate transformers. Recently the author has introduced
state-and-effect triangles which capture this situation categorically,
involving an adjunction between state- and predicate-transformers. The current
paper exploits a classical result in category theory, part of Jon Beck's
monadicity theorem, to systematically construct such a state-and-effect
triangle from an adjunction. The power of this construction is illustrated in
many examples, covering many monads occurring in program semantics, including
(probabilistic) power domains
Enriched lower separation axioms and the principle of enriched continuous extension
[EN] This paper presents a version of the lower separation axioms and the principle of enriched continuous extension for quantale-enriched topological spaces. As a remarkable result, among other things, we point out that in the case of commutative Girard quantales the principle of continuous extension holds for projective modules in Sup.The authors acknowledge support from the Basque Government (grant IT1483-22). The first named author also acknowledges support from a postdoctoral fellowship of the Basque Government (grant POS-2022-1-0015)
Brain Tumor Segmentation with Deep Neural Networks
In this paper, we present a fully automatic brain tumor segmentation method
based on Deep Neural Networks (DNNs). The proposed networks are tailored to
glioblastomas (both low and high grade) pictured in MR images. By their very
nature, these tumors can appear anywhere in the brain and have almost any kind
of shape, size, and contrast. These reasons motivate our exploration of a
machine learning solution that exploits a flexible, high capacity DNN while
being extremely efficient. Here, we give a description of different model
choices that we've found to be necessary for obtaining competitive performance.
We explore in particular different architectures based on Convolutional Neural
Networks (CNN), i.e. DNNs specifically adapted to image data.
We present a novel CNN architecture which differs from those traditionally
used in computer vision. Our CNN exploits both local features as well as more
global contextual features simultaneously. Also, different from most
traditional uses of CNNs, our networks use a final layer that is a
convolutional implementation of a fully connected layer which allows a 40 fold
speed up. We also describe a 2-phase training procedure that allows us to
tackle difficulties related to the imbalance of tumor labels. Finally, we
explore a cascade architecture in which the output of a basic CNN is treated as
an additional source of information for a subsequent CNN. Results reported on
the 2013 BRATS test dataset reveal that our architecture improves over the
currently published state-of-the-art while being over 30 times faster
- …