A Mathematical Unification of Geometric Crossovers Defined on Phenotype Space

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. This paper is motivated by the fact that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. In this paper, we study a metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many example applications of the quotient geometric crossover

CSM-467: Quotient Geometric Crossovers

Geometric crossover is a representation-independent definition of crossover based on the distance of the search space interpreted as a metric space. It generalizes the traditional crossover for binary strings and other important recombination operators for the most frequently used representations. Using a distance tailored to the problem at hand, the abstract definition of crossover can be used to design new problem specific crossovers that embed problem knowledge in the search. In previous work we have started studying how metric transformations of the distance associated with geometric crossover affect the original geometric crossover. In particular, we focused on the product of metric spaces. This metric transformation gives rise to the notion of product geometric crossover that allows to build new geometric crossovers combining pre-existing geometric crossovers in a simple way. In this paper, we study another metric transformation, the quotient metric space, that gives rise to the notion of quotient geometric crossover. This turns out to be a very versatile notion. We give many examples of application of the quotient geometric crossover

CSM-466: Geometric Crossovers for Real-code Representation

Geometric crossover is a representation-independent generalization of the class of traditional mask-based crossover for binary strings. It is based on the distance of the search space seen as a metric space. Although real-code representation allows for a very familiar notion of distance, namely the Euclidean distance, there are also other distances suiting it. Also, topological transformations of the real space give rise to further notions of distance. In this paper, we study the geometric crossovers associated with these distances in a formal and very general setting and show that many preexisting genetic operators for the real-code representation are geometric crossovers. We also propose a novel methodology to remove the inherent bias of pre-existing geometric operators by formally transforming topologies to have the same effect as gluing boundaries

Mathematical Interpretation between Genotype and Phenotype Spaces and Induced Geometric Crossovers

In this paper, we present that genotype-phenotype mapping can be theoretically interpreted using the concept of quotient space in mathematics. Quotient space can be considered as mathematically-defined phenotype space in the evolutionary computation theory. The quotient geometric crossover has the effect of reducing the search space actually searched by geometric crossover, and it introduces problem knowledge in the search by using a distance better tailored to the specific solution interpretation. Quotient geometric crossovers are directly applied to the genotype space but they have the effect of the crossovers performed on phenotype space. We give many example applications of the quotient geometric crossover

Pathologic Findings of Amyloidosis: Recent Advances

Amyloids are aggregations of misfolded protein, which creates fibrillary structures. Unlike normally folded proteins, misfolded fibrils are insoluble and deposited extracellularly or intracellularly. The pathologic mechanism is still unclear, but resultant toxic oligomers within the tissue are known to damage the tissue via aberrant protein interactions. This condition has been known as amyloidosis. Different kinds of amyloid protein may cause similar or different clinical signs and symptoms, largely depending on the target organ it is deposited. However, because treatments and prognoses of each type are different drastically, it is critical to distinguish them and determine the specific type of amyloidosis. The confirmation and typing of amyloid heavily depend on pathologic examination of tissue. The gold standard method for the former is a Congo red staining and birefringence under polarized microscopy. The conventional way for the latter is immunohistochemistry (IHC), where most of the amyloid types can be classified. However, electron microscopy, mass spectrometry, or other molecular methods are required for typing some amyloids that are difficult to identify through IHC. In this chapter, we will describe basic concepts of amyloidosis and pathologic findings of amyloid deposition, including atypical structural deposition. Furthermore, we will review methodologies for amyloid typing briefly

A Giant Maxillary Mucocele Presenting Left Cheek Swelling

A paranasal sinus mucocele is an epithelial-lined, mucus-containing sac that completely fills the sinus and forms an expandable cystic structure. It most commonly affects the frontal and ethmoidal sinuses, and rarely the maxillary and sphenoid sinuses. Orbital displacement or external disfigurement resulting from the expansion of the frontal or ethmoid sinuses is common; however, facial asymmetry caused by maxillary bone remodeling is rare. We describe a case of large maxillary sinus mucocele that destroyed the maxillary sinus bony wall, resulting in notable left cheek swelling and disfigurement, and review the relevant literature

A New Adaptive Hungarian Mating Scheme in Genetic Algorithms

In genetic algorithms, selection or mating scheme is one of the important operations. In this paper, we suggest an adaptive mating scheme using previously suggested Hungarian mating schemes. Hungarian mating schemes consist of maximizing the sum of mating distances, minimizing the sum, and random matching. We propose an algorithm to elect one of these Hungarian mating schemes. Every mated pair of solutions has to vote for the next generation mating scheme. The distance between parents and the distance between parent and offspring are considered when they vote. Well-known combinatorial optimization problems, the traveling salesperson problem, and the graph bisection problem are used for the test bed of our method. Our adaptive strategy showed better results than not only pure and previous hybrid schemes but also existing distance-based mating schemes