Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra

Dynamics of a quantum system can be described by coupled Heisenberg equations. In a generic many-body system these equations form an exponentially large hierarchy that is intractable without approximations. In contrast, in an integrable system a small subset of operators can be closed with respect to commutation with the Hamiltonian. As a result, the Heisenberg equations for these operators can form a smaller closed system amenable to an analytical treatment. We demonstrate that this indeed happens in a class of integrable models where the Hamiltonian is an element of the Onsager algebra. We explicitly solve the system of Heisenberg equations for operators from this algebra. Two specific models are considered as examples: the transverse field Ising model and the superintegrable chiral 3-state Potts model.

Little hierarchy in the minimally specified MSSM

We study constrained versions of the minimal supersymmetric model and investigate the hierarchy between the electroweak scale and the scale of superpartners that can be achieved without relying on specifying model parameters by more than one digit (or with better than 10% precision). This approach automatically avoids scenarios in which a large hierarchy is obtained by special choices of parameters and yet keeps scenarios that would otherwise be disfavored by various sensitivity measures. We consider models with universal gaugino and scalar masses, models with nonuniversal Higgs masses or nonuniversal gaugino masses and focus on scenarios in which all the model parameters are either of the same order or zero at the grand unification scale. We find that the maximal hierarchy between the electroweak scale and stop masses, requiring that model parameters are not specified beyond one digit, ranges from a factor of [Formula: see text][Formula: see text]10–30 for the CMSSM up to [Formula: see text][Formula: see text]300 for models with nonuniversal Higgs or gaugino masses.

Scalable quality assurance for large SNOMED CT hierarchies using subject-based subtaxonomies

Objective Standards terminologies may be large and complex, making their quality assurance challenging. Some terminology quality assurance (TQA) methodologies are based on abstraction networks (AbNs), compact terminology summaries. We have tested AbNs and the performance of related TQA methodologies on small terminology hierarchies. However, some standards terminologies, for example, SNOMED, are composed of very large hierarchies. Scaling AbN TQA techniques to such hierarchies poses a significant challenge. We present a scalable subject-based approach for AbN TQA. Methods An innovative technique is presented for scaling TQA by creating a new kind of subject-based AbN called a subtaxonomy for large hierarchies. New hypotheses about concentrations of erroneous concepts within the AbN are introduced to guide scalable TQA. Results We test the TQA methodology for a subject-based subtaxonomy for the Bleeding subhierarchy in SNOMED's large Clinical finding hierarchy. To test the error concentration hypotheses, three domain experts reviewed a sample of 300 concepts. A consensus-based evaluation identified 87 erroneous concepts. The subtaxonomy-based TQA methodology was shown to uncover statistically significantly more erroneous concepts when compared to a control sample. Discussion The scalability of TQA methodologies is a challenge for large standards systems like SNOMED. We demonstrated innovative subject-based TQA techniques by identifying groups of concepts with a higher likelihood of having errors within the subtaxonomy. Scalability is achieved by reviewing a large hierarchy by subject. Conclusions An innovative methodology for scaling the derivation of AbNs and a TQA methodology was shown to perform successfully for the largest hierarchy of SNOMED.

SOFT SUPERSYMMETRY BREAKING MASSES AND μ PARAMETER FROM DYNAMICAL REARRANGEMENT OF EXOTIC U(1) SYMMETRIES

We propose a mechanism that the soft supersymmetry breaking masses and μ parameter can be induced from the dynamical rearrangement of local U(1) symmetries in a five-dimensional model. It offers to a solution to μ problem if there is a large hierarchy among the relevant U(1) charge of Higgsinos and that of hidden fields which stabilize the extra-dimensional component of U(1) gauge boson.

Document representations for classification of short web-page descriptions

Motivated by applying Text Categorization to classification of Web search results, this paper describes an extensive experimental study of the impact of bag-of- words document representations on the performance of five major classifiers - Na?ve Bayes, SVM, Voted Perceptron, kNN and C4.5. The texts, representing short Web-page descriptions sorted into a large hierarchy of topics, are taken from the dmoz Open Directory Web-page ontology, and classifiers are trained to automatically determine the topics which may be relevant to a previously unseen Web-page. Different transformations of input data: stemming, normalization, logtf and idf, together with dimensionality reduction, are found to have a statistically significant improving or degrading effect on classification performance measured by classical metrics - accuracy, precision, recall, F1 and F2. The emphasis of the study is not on determining the best document representation which corresponds to each classifier, but rather on describing the effects of every individual transformation on classification, together with their mutual relationships. .

Multiple Foci Visualisation of Large Hierarchies with FlexTree

One of the main tasks in information visualisation research is creating visual tools to facilitate human understanding of large and complex information spaces. Hierarchies, being a good mechanism for organising such information, are ubiquitous. Although much research effort has been spent on finding useful representations for hierarchies, visualising large hierarchies is still a difficult topic. One of the difficulties is how to handle the ever increasing scale of hierarchies. Another is how to enable the user to focus on multiple selections of interest while maintaining context. This paper describes a hierarchy visualisation technique called FlexTree to address these problems. It contains some important features that have not been exploited so far. A profile or contour unique to the hierarchy being visualised can be viewed in a bar chart layout. A normalised view of a common attribute of all nodes can be selected by the user. Multiple foci are consistently accessible within a global context through interaction. Furthermore it can handle a large hierarchy that contains 10,000 nodes in a PC environment. This technique has been applied to visualise computer file system structures and decision trees from data mining results. The results from informal user evaluations against these two applications are also presented. User feedback suggests that FlexTree is suitable for visualising large decision trees.