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For each compact subset K of the complex plane C which does not surround zero, the Riemann surface Sζ of the Riemann zeta function restricted to the critical half-strip 0 < Rs < 1/2 contains infinitely many schlicht copies of K lying ‘over’ K. If Sζ also contains at least one such copy, for some K which surrounds zero, then the Riemann hypothesis fails.
A method for the multivariate analysis of statistical phase synchronization phenomena in empirical data is presented. A first statistical approach is complemented by a stochastic dynamic model, to result in a data analysis algorithm which can in a specific sense be shown to be a generic multivariate statistical phase synchronization analysis. The method is applied to EEG data from a psychological experiment, obtaining results which indicate the relevance of this method in the context of cognitive science as well as in other fields.
ANNIS
(2004)
In this paper, we discuss the design and implementation of our first version of the database "ANNIS" ("ANNotation of Information Structure"). For research based on empirical data, ANNIS provides a uniform environment for storing this data together with its linguistic annotations. A central database promotes standardized annotation, which facilitates interpretation and comparison of the data. ANNIS is used through a standard web browser and offers tier-based visualization of data and annotations, as well as search facilities that allow for cross-level and cross-sentential queries. The paper motivates the design of the system, characterizes its user interface, and provides an initial technical evaluation of ANNIS with respect to data size and query processing.
Berlin : look to the world!
(2004)
In the spring 2004 issue of WeltTrends, Professor Gunther Hellmann made a „plea for offensive idealism“ and „against the power political resocialization of German foreign policy“. To a long-time outside observer of that foreign policy, this plea is unsurprising, but depressing. In keeping with Professor Hellmann’s own willingness, „notwendige Differenzierungen [zu] vernachlässigen zugunsten einer bewussten Zuspitzung“ I will comment on the aspects of his argument that strike an American colleague as particularly disturbing.
Edge representations of operators on closed manifolds are known to induce large classes of operators that are elliptic on specific manifolds with edges, cf. [9]. We apply this idea to the case of boundary value problems. We establish a correspondence between standard ellipticity and ellipticity with respect to the principal symbolic hierarchy of the edge algebra of boundary value problems, where an embedded submanifold on the boundary plays the role of an edge. We first consider the case that the weight is equal to the smoothness and calculate the dimensions of kernels and cokernels of the associated principal edge symbols. Then we pass to elliptic edge operators for arbitrary weights and construct the additional edge conditions by applying relative index results for conormal symbols.
We first introduce some coupling of a finite number of Probabilistic Cellular Automata dynamics (PCA), preserving the stochastic ordering. Using this tool, for a general attractive probabilistic cellular automata on SZd, where S is finite, we prove that a condition (A) is equivalent to the (time-) convergence towards equilibrium of this Markovian parallel dynamics, in the uniform norm, exponentially fast. This condition (A) means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite ‘box’-volume. For a class of reversible PCA dynamics on {−1, +1}Zd , with a naturally associated Gibbsian potential ϕ, we prove that a Weak Mixing condition for ϕ implies the validity of the assumption (A); thus the ‘exponential ergodicity’ of the dynamics towards the unique Gibbs measure associated to ϕ holds. On some particular examples of this PCA class, we verify that our assumption (A) is weaker than the Dobrushin-Vasershtein ergodicity condition. For some special PCA, the ‘exponential ergodicity’ holds as soon as there is no phase transition.
This paper investigates the nature of the attraction of XPs to clauseinitial position in German (and other languages). It argues that there are two different types of preposing. First, an XP can move when it is attracted by an EPP-like feature of Comp. Comp can, however, also attract elements that bear the formal marker of some semantic or pragmatic (information theoretic) function. This second type of movement is driven by the attraction of a formal property of the moved element. It has often been misanalysed as “operator” movement in the past. Japanese wh-questions always exhibit focus intonation (FI). Furthermore, the domain of FI exhibits a correspondence to the wh-scope. I propose that this phonology-semantics correspondence is a result of the cyclic computation of FI, which is explained under the notion of Multiple Spell-Out in the recent Minimalist framework. The proposed analysis makes two predictions: (1) embedding of an FI into another is possible; (2) (overt) movement of a wh-phrase to a phase edge position causes a mismatch between FI and wh-scope. Both predictions are tested experimentally, and shown to be borne out.
Content: 1 The Typology 1.1 Object Placement 2 Treatment of StG in terms of LF Movement – with and without Head Movement 3 An OT-solution in terms of linearisation (‘LF-to-PF-Mapping’) 3.1 The trigger for additional orders: Focus 3.2 Competitions 3.3 Summary 4 RP 4.1 LF Movement – with and without Head Movement 4.2 The OT-account for RP 4.3 Competitions 5 Summary
Contents: Chapter 6: Elliptic Theory on Manifolds with Edges Introduction 6.1. Motivation and Main Constructions 6.1.1. Manifolds with edges 6.1.2. Edge-degenerate differential operators 6.1.3. Symbols 6.1.4. Elliptic problems 6.2. Pseudodifferential Operators 6.2.1. Edge symbols 6.2.2. Pseudodifferential operators 6.2.3. Quantization 6.3. Elliptic Morphisms and the Finiteness Theorem 6.3.1. Matrix Green operators 6.3.2. General morphisms 6.3.3. Ellipticity, Fredholm property, and smoothness Appendix A. Fiber Bundles and Direct Integrals A.1. Local theory A.2. Globalization A.3. Versions of the Definition of the Norm
Contents: Chapter 7: The Index Problemon Manifolds with Singularities Preface 7.1. The Simplest Index Formulas 7.1.1. General properties of the index 7.1.2. The index of invariant operators on the cylinder 7.1.3. Relative index formulas 7.1.4. The index of general operators on the cylinder 7.1.5. The index of operators of the form 1 + G with a Green operator G 7.1.6. The index of operators of the form 1 + G on manifolds with edges 7.1.7. The index on bundles with smooth base and fiber having conical points 7.2. The Index Problem for Manifolds with Isolated Singularities 7.2.1. Statement of the index splitting problem 7.2.2. The obstruction to the index splitting 7.2.3. Computation of the obstruction in topological terms 7.2.4. Examples. Operators with symmetries 7.3. The Index Problem for Manifolds with Edges 7.3.1. The index excision property 7.3.2. The obstruction to the index splitting 7.4. Bibliographical Remarks
We study a natural Dirac operator on a Lagrangian submanifold of a Kähler manifold. We first show that its square coincides with the Hodge - de Rham Laplacian provided the complex structure identifies the Spin structures of the tangent and normal bundles of the submanifold. We then give extrinsic estimates for the eigenvalues of that operator and discuss some examples.
In this paper we review the current state of research on the issue of discourse structure (DS)/information structure (IS) interface. This field has received a lot of attention from discourse semanticists and pragmatists, and has made substantial progress in recent years. In this paper we summarize the relevant studies. In addition, we look at the issue of DS/ISinteraction at a different level - that of phonetics. It is known that both information structure and discourse structure can be realized prosodically, but the issue of phonetic interaction between the prosodic devices they employ has hardly ever been discussed in this context. We think that a proper consideration of this aspect of DS/IS-interaction would enrich our understanding of the phenomenon, and hence we formulate some related research-programmatic positions.
The ellipticity of operators on a manifold with edge is defined as the bijectivity of the components of a principal symbolic hierarchy σ = (σψ, σ∧), where the second component takes value in operators on the infinite model cone of the local wedges. In general understanding of edge problems there are two basic aspects: Quantisation of edge-degenerate operators in weighted Sobolev spaces, and verifying the elliptcity of the principal edge symbol σ∧ which includes the (in general not explicitly known) number of additional conditions on the edge of trace and potential type. We focus here on these queations and give explicit answers for a wide class of elliptic operators that are connected with the ellipticity of edge boundary value problems and reductions to the boundary. In particular, we study the edge quantisation and ellipticity for Dirichlet-Neumann operators with respect to interfaces of some codimension on a boundary. We show analogues of the Agranovich-Dynin formula for edge boundary value problems, and we establish relations of elliptic operators for different weights, via the spectral flow of the underlying conormal symbols.
Ergodicity of PCA
(2004)
For a general attractive Probabilistic Cellular Automata on S-Zd, we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A). This condition means the exponential decay of the influence from the boundary for the invariant measures of the system restricted to finite boxes. For a class of reversible PCA dynamics on {1,+1}(Zd), wit a naturally associated Gibbsian potential rho, we prove that a (spatial-) weak mixing condition (WM) for rho implies the validity of the assumption (A); thus exponential (time-) ergodicity of these dynamics towards the unique Gibbs measure associated to rho hods. On some particular examples we state that exponential ergodicity holds as soon as there is no phase transition.
Focus strategies in chadic
(2004)
We argue that the standard focus theories reach their limits when confronted with the focus systems of the Chadic languages. The backbone of the standard focus theories consists of two assumptions, both called into question by the languages under consideration. Firstly, it is standardly assumed that focus is generally marked by stress. The Chadic languages, however, exhibit a variety of different devices for focus marking. Secondly, it is assumed that focus is always marked. In Tangale, at least, focus is not marked consistently on all types of constituents. The paper offers two possible solutions to this dilemma.
How do children determine the syntactic category of novel words? In this article we present the results of 2 experiments that investigated whether German children between 12 and 16 months of age can use distributional knowledge that determiners precede nouns and subject pronouns precede verbs to syntactically categorize adjacent novel words. Evidence from the head-turn preference paradigm shows that, although 12- to 13-month-olds cannot do this, 14- to 16-month-olds are able to use a determiner to categorize a following novel word as a noun. In contrast, no categorization effect was found for a novel word following a subject pronoun. To understand this difference we analyzed adult child-directed speech. This analysis showed that there are in fact stronger co-occurrence relations between determiners and nouns than between subject pronouns and verbs. Thus, in German determiners may be more reliable cues to the syntactic category of an adjacent novel word than are subject pronouns. We propose that the capacity to syntactically categorize novel words, demonstrated here for the first time in children this young, mediates between the recognition of the specific morphosyntactic frame in which a novel word appears and the word-to-world mapping that is needed to build up a semantic representation for the novel word.
Results of a production experiment on the placement of sentence accent in German are reported. The hypothesis that German fulfills some of the most widely accepted rules of accent assignment— predicting focus domain integration—was only partly confirmed. Adjacency between argument and verb induces a single accent on the argument, as recognized in the literature, but interruption of this sequence by a modifier often induces remodeling of the accent pattern with a single accent on the modifier. The verb is rarely stressed. All models based on linear alignment or adjacency between elements belonging to a single accent domain fail to account for this result. A cyclic analysis of prosodic domain formation is proposed in an optimality-theoretic framework that can explain the accent pattern. Japanese wh-questions always exhibit focus intonation (FI). Furthermore, the domain of FI exhibits a correspondence to the wh-scope. I propose that this phonology-semantics correspondence is a result of the cyclic computation of FI, which is explained under the notion of Multiple Spell-Out in the recent Minimalist framework. The proposed analysis makes two predictions: (1) embedding of an FI into another is possible; (2) (overt) movement of a wh-phrase to a phase edge position causes a mismatch between FI and wh-scope. Both predictions are tested experimentally, and shown to be borne out.