Multi-Dimensional Inheritance

In this paper, we present an alternative approach to multiple inheritance for typed feature structures. In our approach, a feature structure can be associated with several types coming from different hierarchies (dimensions). In case of multiple inheritance, a type has supertypes from different hierarchies. We contrast this approach with approaches based on a single type hierarchy where a feature structure has only one unique most general type, and multiple inheritance involves computation of greatest lower bounds in the hierarchy. The proposed approach supports current linguistic analyses in constraint-based formalisms like HPSG, inheritance in the lexicon, and knowledge representation for NLP systems. Finally, we show that multi-dimensional inheritance hierarchies can be compiled into a Prolog term representation, which allows to compute the conjunction of two types efficiently by Prolog term unification.Comment: 9 pages, styles: a4,figfont,eepic,eps

Solvable Markovian dynamics of lattice quantum spin models

We address the real-time dynamics of lattice quantum spin models coupled to single or multiple Markovian dissipative reservoirs using the method of closed hierarchies of correlation functions. This approach allows us to solve a number of quantum spin models exactly in arbitrary dimensions, which is illustrated explicitly with two examples of driven-dissipative systems. We investigate their respective nonequilibrium steady states as well as the full real-time evolution on unprecedented system sizes. Characteristic time scales are derived analytically, which allows us to understand the nontrivial finite-size scaling of the dissipative gap. The corresponding scaling exponents are confirmed by solving numerically for the full real-time evolution of two-point correlation functions.Comment: 6 pages, 2 figures; version accepted for publication in PR

The Flavour Hierarchy and See-Saw Neutrinos from Bulk Masses in 5d Orbifold GUTs

In supersymmetric grand unified theories (GUTs) based on S^1/(Z_2 x Z'_2) orbifold constructions in 5 dimensions, Standard Model (SM) matter and Higgs fields can be realized in terms of 5d hypermultiplets. These hypermultiplets can naturally have large bulk masses, leading to a localization of the zero modes at one of the two branes or to an exponential suppression of the mass of the lowest-lying non-zero mode. We demonstrate that these dynamical features allow for the construction of an elegant 3-generation SU(5) model in 5 dimensions that explains all the hierarchies between fermion masses and CKM matrix elements in geometrical terms. Moreover, if U(1)_\chi (where SU(5) x U(1)_\chi \subset SO(10)) is gauged in the bulk, but broken by the orbifold action at the SM brane, the right-handed neutrino mass scale is naturally suppressed relative to M_GUT. Together with our construction in the charged fermion sector this leads, via the usual see-saw mechanism, to a realistic light neutrino mass scale and large neutrino mixing angles.Comment: 10 pages LaTeX, 1 figure. Minor comments and reference added. Version to be published in PL

Parallel Hierarchies: Interactive Visualization of Multidimensional Hierarchical Aggregates

Exploring multi-dimensional hierarchical data is a long-standing problem present in a wide range of fields such as bioinformatics, software systems, social sciences and business intelligence. While each hierarchical dimension within these data structures can be explored in isolation, critical information lies in the relationships between dimensions. Existing approaches can either simultaneously visualize multiple non-hierarchical dimensions, or only one or two hierarchical dimensions. Yet, the challenge of visualizing multi-dimensional hierarchical data remains open. To address this problem, we developed a novel data visualization approach -- Parallel Hierarchies -- that we demonstrate on a real-life SAP SE product called SAP Product Lifecycle Costing. The starting point of the research is a thorough customer-driven requirement engineering phase including an iterative design process. To avoid restricting ourselves to a domain-specific solution, we abstract the data and tasks gathered from users, and demonstrate the approach generality by applying Parallel Hierarchies to datasets from bioinformatics and social sciences. Moreover, we report on a qualitative user study conducted in an industrial scenario with 15 experts from 9 different companies. As a result of this co-innovation experience, several SAP customers requested a product feature out of our solution. Moreover, Parallel Hierarchies integration as a standard diagram type into SAP Analytics Cloud platform is in progress. This thesis further introduces different uncertainty representation methods applicable to Parallel Hierarchies and in general to flow diagrams. We also present a visual comparison taxonomy for time-series of hierarchically structured data with one or multiple dimensions. Moreover, we propose several visual solutions for comparing hierarchies employing flow diagrams. Finally, after presenting two application examples of Parallel Hierarchies on industrial datasets, we detail two validation methods to examine the effectiveness of the visualization solution. Particularly, we introduce a novel design validation table to assess the perceptual aspects of eight different visualization solutions including Parallel Hierarchies.:1 Introduction 1.1 Motivation and Problem Statement 1.2 Research Goals 1.3 Outline and Contributions 2 Foundations of Visualization 2.1 Information Visualization 2.1.1 Terms and Definition 2.1.2 What: Data Structures 2.1.3 Why: Visualization Tasks 2.1.4 How: Visualization Techniques 2.1.5 How: Interaction Techniques 2.2 Visual Perception 2.2.1 Visual Variables 2.2.2 Attributes of Preattentive and Attentive Processing 2.2.3 Gestalt Principles 2.3 Flow Diagrams 2.3.1 Classifications of Flow Diagrams 2.3.2 Main Visual Features 2.4 Summary 3 Related Work 3.1 Cross-tabulating Hierarchical Categories 3.1.1 Visualizing Categorical Aggregates of Item Sets 3.1.2 Hierarchical Visualization of Categorical Aggregates 3.1.3 Visualizing Item Sets and Their Hierarchical Properties 3.1.4 Hierarchical Visualization of Categorical Set Aggregates 3.2 Uncertainty Visualization 3.2.1 Uncertainty Taxonomies 3.2.2 Uncertainty in Flow Diagrams 3.3 Time-Series Data Visualization 3.3.1 Time & Data 3.3.2 User Tasks 3.3.3 Visual Representation 3.4 Summary ii Contents 4 Requirement Engineering Phase 4.1 Introduction 4.2 Environment 4.2.1 The Product 4.2.2 The Customers and Development Methodology 4.2.3 Lessons Learned 4.3 Visualization Requirements for Product Costing 4.3.1 Current Visualization Practice 4.3.2 Visualization Tasks 4.3.3 Data Structure and Size 4.3.4 Early Visualization Prototypes 4.3.5 Challenges and Lessons Learned 4.4 Data and Task Abstraction 4.4.1 Data Abstraction 4.4.2 Task Abstraction 4.5 Summary and Outlook 5 Parallel Hierarchies 5.1 Introduction 5.2 The Parallel Hierarchies Technique 5.2.1 The Individual Axis: Showing Hierarchical Categories 5.2.2 Two Interlinked Axes: Showing Pairwise Frequencies 5.2.3 Multiple Linked Axes: Propagating Frequencies 5.2.4 Fine-tuning Parallel Hierarchies through Reordering 5.3 Design Choices 5.4 Applying Parallel Hierarchies 5.4.1 US Census Data 5.4.2 Yeast Gene Ontology Annotations 5.5 Evaluation 5.5.1 Setup of the Evaluation 5.5.2 Procedure of the Evaluation 5.5.3 Results from the Evaluation 5.5.4 Validity of the Evaluation 5.6 Summary and Outlook 6 Visualizing Uncertainty in Flow Diagrams 6.1 Introduction 6.2 Uncertainty in Product Costing 6.2.1 Background 6.2.2 Main Causes of Bad Quality in Costing Data 6.3 Visualization Concepts 6.4 Uncertainty Visualization using Ribbons 6.4.1 Selected Visualization Techniques 6.4.2 Study Design and Procedure 6.4.3 Results 6.4.4 Discussion 6.5 Revised Visualization Approach using Ribbons 6.5.1 Application to Sankey Diagram 6.5.2 Application to Parallel Sets 6.5.3 Application to Parallel Hierarchies 6.6 Uncertainty Visualization using Nodes 6.6.1 Visual Design of Nodes 6.6.2 Expert Evaluation 6.7 Summary and Outlook 7 Visual Comparison Task 7.1 Introduction 7.2 Comparing Two One-dimensional Time Steps 7.2.1 Problem Statement 7.2.2 Visualization Design 7.3 Comparing Two N-dimensional Time Steps 7.4 Comparing Several One-dimensional Time Steps 7.5 Summary and Outlook 8 Parallel Hierarchies in Practice 8.1 Application to Plausibility Check Task 8.1.1 Plausibility Check Process 8.1.2 Visual Exploration of Machine Learning Results 8.2 Integration into SAP Analytics Cloud 8.2.1 SAP Analytics Cloud 8.2.2 Ocean to Table Project 8.3 Summary and Outlook 9 Validation 9.1 Introduction 9.2 Nested Model Validation Approach 9.3 Perceptual Validation of Visualization Techniques 9.3.1 Design Validation Table 9.3.2 Discussion 9.4 Summary and Outlook 10 Conclusion and Outlook 10.1 Summary of Findings 10.2 Discussion 10.3 Outlook A Questionnaires of the Evaluation B Survey of the Quality of Product Costing Data C Questionnaire of Current Practice Bibliograph

Collider Signature of Bulk Neutrinos in Large Extra Dimensions

We consider the collider signature of right-handed neutrinos propagating in $\delta$ (large) extra dimensions, and interacting with Standard Model fields only through a Yukawa coupling to the left-handed neutrino and the Higgs boson. These theories are attractive as they can explain the smallness of the neutrino mass, as has already been shown. We show that if $\delta$ is bigger than two, it can result in an enhancement in the production rate of the Higgs boson, decaying either invisibly or to a $b$ anti-$b$ quark pair, associated with an isolated high $p_T$ charged lepton and missing transverse energy at future hadron colliders, such as the LHC. The enhancement is due to the large number of Kaluza-Klein neutrinos produced in the final state. The observation of the signal event would provide an opportunity to distinguish between the normal and inverted neutrino mass hierarchies, and to determine the absolute scale of neutrino masses by measuring the asymmetry of the observed event numbers in the electron and muon channels.Comment: 31 pages, 13 figures. v2: Added discussion on PDF uncertainties, added reference

Yukawa Hierarchies in Global F-theory Models

We argue that global F-theory compactifications to four dimensions generally exhibit higher rank Yukawa matrices from multiple geometric contributions known as Yukawa points. The holomorphic couplings furthermore have large hierarchies for generic complex structure moduli. Unlike local considerations, the compact setup realizes these features all through geometry, and requires no instanton corrections. As an example, we consider a concrete toy model with $SU(5) \times U(1)$ gauge symmetry. From the geometry, we find two Yukawa points for the ${\bf 10}_{-2} \, \bar{\bf 5}_6 \, \bar{\bf 5}_{-4}$ coupling, producing a rank two Yukawa matrix. Our methods allow us to track all complex structure dependencies of the holomorphic couplings and study the ratio numerically. This reveals hierarchies of ${\cal O}(10^5)$ and larger on a full-dimensional subspace of the moduli space.Comment: 25 pages + appendix and references; v2: matched published version (typos corrected

Singular Vectors and Topological Theories from Virasoro Constraints via the Kontsevich-Miwa Transform

We use the Kontsevich-Miwa transform to relate the different pictures describing matter coupled to topological gravity in two dimensions: topological theories, Virasoro constraints on integrable hierarchies, and a DDK-type formalism. With the help of the Kontsevich-Miwa transform, we solve the Virasoro constraints on the KP hierarchy in terms of minimal models dressed with a (free) Liouville-like scalar. The dressing prescription originates in a topological (twisted N=2) theory. The Virasoro constraints are thus related to essentially the N=2 null state decoupling equations. The N=2 generators are constructed out of matter, the `Liouville' scalar, and $c=-2$ ghosts. By a `dual' construction involving the reparametrization $c=-26$ ghosts, the DDK dressing prescription is reproduced from the N=2 symmetry. As a by-product we thus observe that there are two ways to dress arbitrary $d\leq1$ or $d\geq25$ matter theory, that allow its embedding into a topological theory. By th e Kontsevich-Miwa transform, which introduces an infinite set of `time' variables $t_r$, the equations ensuring the vanishing of correlators that involve BRST-exact primary states, factorize through the Virasoro generators expressed in terms of the $t_r$. The background charge of these Virasoro generators is determined by the topological central charge.Comment: 62p. LaTeX, CERN-TH.6752, IMAFF-92/8, revised (minor corrections, typos) easy-fontversio