Some Lattice Problems In Fuzzy Set Theory And Fuzzy Topology

It is believed that every fuzzy generalization should be formulated in such a way that it contain the ordinary set theoretic notion as a special case. Therefore the definition of fuzzy topology in the line of C.L.CHANG E9] with an arbitrary complete and distributive lattice as the membership set is taken. Almost all the results proved and presented in this thesis can, in a sense, be called generalizations of corresponding results in ordinary set theory and set topology. However the tools and the methods have to be in many of the cases, new. Here an attempt is made to solve the problem of complementation in the lattice of fuzzy topologies on a set. It is proved that in general, the lattice of fuzzy topologies is not complemented. Complements of some fuzzy topologies are found out. It is observed that (L,X) is not uniquely complemented. However, a complete analysis of the problem of complementation in the lattice of fuzzy topologies is yet to be found out

Prediction of Key Symptoms of Learning Disabilities in School-Age Children Using Rough Sets

This paper highlights the prediction of learning disabilities (LD) in school-age children using rough set theory (RST) with an emphasis on application of data mining. In rough sets, data analysis start from a data table called an information system, which contains data about objects of interest, characterized in terms of attributes. These attributes consist of the properties of learning disabilities. By finding the relationship between these attributes, the redundant attributes can be eliminated and core attributes determined. Also, rule mining is performed in rough sets using the algorithm LEM1. The prediction of LD is accurately done by using Rosetta, the rough set tool kit for analysis of data. The result obtained from this study is compared with the output of a similar study conducted by us using Support Vector Machine (SVM) with Sequential Minimal Optimisation (SMO) algorithm. It is found that, using the concepts of reduct and global covering, we can easily predict the learning disabilities in children

Maximal compactness, min- imal Hausdor ness and reversibility of frames and a study on automorphism group of frames

One can do research in pointfree topology in two ways. The rst is the contravariant way where research is done in the category Frm but the ultimate objective is to obtain results in Loc. The other way is the covariant way to carry out research in the category Loc itself directly. According to Johnstone [23], \frame theory is lattice theory applied to topology whereas locale theory is topology itself". The most part of this thesis is written according to the rst view. In this thesis, we make an attempt to study about 1. the frame counterparts of maximal compactness, minimal Hausdor - ness and reversibility, 2. the automorphism groups of a nite frame and its relation with the subgroups of the permutation group on the generator set of the frame

Test for basis-set errors in relativistic Dirac-Fock-Slater calculations with a numerical AO-DFS-basis

A fully relativistic four-component Dirac-Fock-Slater program for diatomics, with numerically given AO's as basis functions is presented. We discuss the problem of the errors due to the finite basis-set, and due to the influence of the negative energy solutions of the Dirac Hamiltonian. The negative continuum contributions are found to be very small.

Bud development, flowering and fruit set of Moringa oleifera Lam. (Horseradish Tree) as affected by various irrigation levels

Moringa oleifera is becoming increasingly popular as an industrial crop due to its multitude of useful attributes as water purifier, nutritional supplement and biofuel feedstock. Given its tolerance to sub-optimal growing conditions, most of the current and anticipated cultivation areas are in medium to low rainfall areas. This study aimed to assess the effect of various irrigation levels on floral initiation, flowering and fruit set. Three treatments namely, a 900 mm (900IT), 600 mm (600IT) and 300 mm (300IT) per annum irrigation treatment were administered through drip irrigation, simulating three total annual rainfall amounts. Individual inflorescences from each treatment were tagged during floral initiation and monitored throughout until fruit set. Flower bud initiation was highest at the 300IT and lowest at the 900IT for two consecutive growing seasons. Fruit set on the other hand, decreased with the decrease in irrigation treatment. Floral abortion, reduced pollen viability as well as moisture stress in the style were contributing factors to the reduction in fruiting/yield observed at the 300IT. Moderate water stress prior to floral initiation could stimulate flower initiation, however, this should be followed by sufficient irrigation to ensure good pollination, fruit set and yield.

Enlarging a training set for genomic selction by imputation of un-genotyped animals in populations of varying genetic architecture

Background: The most common application of imputation is to infer genotypes of a high-density panel of markers on animals that are genotyped for a low-density panel. However, the increase in accuracy of genomic predictions resulting from an increase in the number of markers tends to reach a plateau beyond a certain density. Another application of imputation is to increase the size of the training set with un-genotyped animals. This strategy can be particularly successful when a set of closely related individuals are genotyped. ----- Methods: Imputation on completely un-genotyped dams was performed using known genotypes from the sire of each dam, one offspring and the offspring’s sire. Two methods were applied based on either allele or haplotype frequencies to infer genotypes at ambiguous loci. Results of these methods and of two available software packages were compared. Quality of imputation under different population structures was assessed. The impact of using imputed dams to enlarge training sets on the accuracy of genomic predictions was evaluated for different populations, heritabilities and sizes of training sets. ----- Results: Imputation accuracy ranged from 0.52 to 0.93 depending on the population structure and the method used. The method that used allele frequencies performed better than the method based on haplotype frequencies. Accuracy of imputation was higher for populations with higher levels of linkage disequilibrium and with larger proportions of markers with more extreme allele frequencies. Inclusion of imputed dams in the training set increased the accuracy of genomic predictions. Gains in accuracy ranged from close to zero to 37.14%, depending on the simulated scenario. Generally, the larger the accuracy already obtained with the genotyped training set, the lower the increase in accuracy achieved by adding imputed dams. ----- Conclusions: Whenever a reference population resembling the family configuration considered here is available, imputation can be used to achieve an extra increase in accuracy of genomic predictions by enlarging the training set with completely un-genotyped dams. This strategy was shown to be particularly useful for populations with lower levels of linkage disequilibrium, for genomic selection on traits with low heritability, and for species or breeds for which the size of the reference population is limited.

Efficient Characterisation and Optimal Control of Open Quantum Systems - Mathematical Foundations and Physical Applications

Since no physical system can ever be completely isolated from its environment, the study of open quantum systems is pivotal to reliably and accurately control complex quantum systems. In practice, reliability of the control field needs to be confirmed via certification of the target evolution while accuracy requires the derivation of high-fidelity control schemes in the presence of decoherence. In the first part of this thesis an algebraic framework is presented that allows to determine the minimal requirements on the unique characterisation of arbitrary unitary gates in open quantum systems, independent on the particular physical implementation of the employed quantum device. To this end, a set of theorems is devised that can be used to assess whether a given set of input states on a quantum channel is sufficient to judge whether a desired unitary gate is realised. This allows to determine the minimal input for such a task, which proves to be, quite remarkably, independent of system size. These results allow to elucidate the fundamental limits regarding certification and tomography of open quantum systems. The combination of these insights with state-of-the-art Monte Carlo process certification techniques permits a significant improvement of the scaling when certifying arbitrary unitary gates. This improvement is not only restricted to quantum information devices where the basic information carrier is the qubit but it also extends to systems where the fundamental informational entities can be of arbitary dimensionality, the so-called qudits. The second part of this thesis concerns the impact of these findings from the point of view of Optimal Control Theory (OCT). OCT for quantum systems utilises concepts from engineering such as feedback and optimisation to engineer constructive and destructive interferences in order to steer a physical process in a desired direction. It turns out that the aforementioned mathematical findings allow to deduce novel optimisation functionals that significantly reduce not only the required memory for numerical control algorithms but also the total CPU time required to obtain a certain fidelity for the optimised process. The thesis concludes by discussing two problems of fundamental interest in quantum information processing from the point of view of optimal control - the preparation of pure states and the implementation of unitary gates in open quantum systems. For both cases specific physical examples are considered: for the former the vibrational cooling of molecules via optical pumping and for the latter a superconducting phase qudit implementation. In particular, it is illustrated how features of the environment can be exploited to reach the desired targets.

Retargeting of pre-set regions on chromosome for high gene expression in mammalian cells

We have developed a system to hunt and reuse special gene integration sites that allow for high and stable gene expression. A vector, named pRGFP8, was constructed. The plasmid pRGFP8 contains a reporter gene, gfp2 and two extraneous DNA fragments. The gene gfp2 makes it possible to screen the high expression regions on the chromosome. The extraneous DNA fragments can help to create the unique loci on the chromosome and increase the gene targeting frequency by increasing the homology. After transfection into Chinese hamster ovary cells (CHO) cells, the linearized pRGFP8 can integrate into the chromosome of the host cells and form the unique sites. With FACS, 90 millions transfected cells were sorted and the cells with strongest GFP expression were isolated, and then 8 stable high expression GFP CHO cell lines were selected as candidates for the new host cell. Taking the unique site created by pRGFP8 on the chromosome in the new host cells as a targeting locus, the gfp2 gene was replaced with the gene of interest, human ifngamma, by transfecting the targeting plasmid pRIH-IFN. Then using FACS, the cells with the dimmest GFP fluorescence were selected. These cells showed they had strong abilities to produce the protein of interest, IFN-gamma. During the gene targeting experiment, we found there is positive correlation between the fluorescence density of the GFP CHO host cells and the specific production rate of IFN-gamma. This result shows that the strategy in our expression system is correct: the production of the interesting protein increases with the increase fluorescence of the GFP host cells. This system, the new host cell lines and the targeting vector, can be utilized for highly expressing the gene of interest. More importantly, by using FACS, we can fully screen all the transfected cells, which can reduce the chances of losing the best cells.

When a data set can be considered compositional?

Traditionally, compositional data has been identified with closed data, and the simplex has been considered as the natural sample space of this kind of data. In our opinion, the emphasis on the constrained nature of compositional data has contributed to mask its real nature. More crucial than the constraining property of compositional data is the scale-invariant property of this kind of data. Indeed, when we are considering only few parts of a full composition we are not working with constrained data but our data are still compositional. We believe that it is necessary to give a more precise definition of composition. This is the aim of this oral contribution

Quantified set inversion with applications to control

This paper describes a new reliable method, based on modal interval analysis (MIA) and set inversion (SI) techniques, for the characterization of solution sets defined by quantified constraints satisfaction problems (QCSP) over continuous domains. The presented methodology, called quantified set inversion (QSI), can be used over a wide range of engineering problems involving uncertain nonlinear models. Finally, an application on parameter identification is presented

Sonic Labyrinths - 3 upon a ground (minimal mix)

Electronic music based on an algorithm, but with a good deal of human influence. See other items with keywords 'sonic labyrinths' for details.

Point Set Topology

Lecture notes about point set toplogy

Team Quintinlessness: Open source software resource set

INFO2009 Assignment 2 reference list for team "Quintinlessness" - Subject: Open source software

Green ICT Resource Set - INFO2009 Coursework, Bobs' Finest Group

Online resource set which details in full the Green ICT topic and associated areas. Online multiple choice quiz also included to test readers knowledge of topic once the tutorial has been read.

INFO2009 Academic Year 09-10: Luc Moreau's Tutor Group's Accessibility Resource Set

Our resource set