Recent research has highlighted the character and importance of the study of agreement. This paper, paralleling work on the more familiar concept of deep disagreement, will provide a first articulation of the character and implications of deep agreements, that is, agreements so deep that disagreement cannot overcome them. To do so, I start by outlining the main features of deep disagreement. I then provide a brief characterization of agreement in general to ground the discussion of the unique characteristics of deep agreements and compare them to deep disagreements. After distinguishing the concept from other more familiar ones, I then point to a few of the major social and theoretical issues the existence of deep agreements poses before concluding with some remarks pointing to valuable areas for future research.

In this paper, we prove the Fukui–Kurdyka–Paunescu conjecture, which says that sub-analytic arc-analytic bi-Lipschitz homeomorphisms preserve the multiplicities of real analytic sets. We also prove several other results on the invariance of the multiplicity (respectively, degree) of real and complex analytic (respectively, algebraic) sets. For instance, still in the real case, we prove a global version of the Fukui–Kurdyka–Paunescu conjecture. In the complex case, one of the results that we prove is the following: if $(X,0)\subset (\mathbb {C}^{n},0)$, $(Y,0)\subset (\mathbb {C}^{m},0)$ are germs of analytic sets and $h\colon (X,0)\to (Y,0)$ is a semi-bi-Lipschitz homeomorphism whose graph is a complex analytic set, then the germs $(X,0)$ and $(Y,0)$ have the same multiplicity. One of the results that we prove in the global case is the following: if $X\subset \mathbb {C}^{n}$, $Y\subset \mathbb {C}^{m}$ are algebraic sets and $\phi \colon X\to Y$ is a semi-algebraic semi-bi-Lipschitz homeomorphism such that the closure of its graph in $\mathbb {P}^{n+m}(\mathbb {C})$ is an orientable homological cycle, then ${\rm deg}(X)={\rm deg}(Y)$.

Upper German dialects make heavy use of diminutive strategies, but little is known about the actual conceptual effects of those devices. This paper is the first to present two large-scale psycholinguistic experiments that investigate this issue in East Franconian, a dialect spoken in Bavaria. Franconian uses both the diminutive suffix -la and the quantifying construction a weng a lit. ‘a little bit a’ to modify noun phrases. Our first experiment shows that diminutization has no effect on conceptualization of magnitude: People do not think of a smaller/weaker/shorter etc. referent when the NP is modified by the morphological diminutive, the quantifying construction, or their combination. The second experiment involves gradable NPs and shows that, again, the morphological diminutive has no effect on how people conceptualize the degree to which a gradable nominal predicate holds; in contrast, a weng a reduces it significantly. These experiments suggest that diminutization does not have uniform effects across semantic domains, and our results act as a successful example of extending the avenue of cognitive psychology into dialectology with the active participation of a speaker community.*

Objective: Previous studies have shown differences in the regional brain structure and function between patients with bipolar disorder (BD) and healthy subjects, but little is known about the structural connectivity between BD patients and healthy subjects. In this study, we evaluated the disease-related changes in regional structural connectivity derived from gray matter magnetic resonance imaging (MRI) scans. Methods: The subjects were 73 patients with BD and 80 healthy volunteers who underwent 3-Tesla MRI. Network metrics, such as the small world properties, were computed. We also performed rendering of the network metric images such as the degree, betweenness centrality, and clustering coefficient, on individual brain image. Then, we estimated the differences between them, and evaluate the relationships between the clinical symptoms and the network metrics in the patients with BD. Results: BD patients showed a lower clustering coefficient in the right parietal region and left occipital region, compared with healthy subjects. A weak negative correlation between Young mania rating scale and clustering coefficient was found in left anterior cingulate cortex. Conclusions: We found differences in gray matter structural connectivity between BD patients and healthy subjects by a similarity-based approach. These points may provide objective biological information as an adjunct to the clinical diagnosis of BD.

We investigate several aspects of a self-similar evolutionary process that builds a random bipolar network from building blocks that are themselves small bipolar networks. We characterize admissible outdegrees in the history of the evolution. We obtain the limit distribution of the polar degrees (when suitably scaled) characterized by its sequence of moments. We also obtain the asymptotic joint multivariate normal distribution of the number of nodes of small admissible outdegrees. Five possible substructures arise, and each has its own parameters (mean vector and covariance matrix) in the multivariate distribution. Several results are obtained by mapping bipolar networks into Pólya urns.

We give algebraic proofs of some results of Wang on homomorphisms of nonzero degree between aspherical closed orientable 3-manifolds. Our arguments apply to PDn-groups which are virtually poly-Z or have a Kropholler decomposition into parts of generalized Seifert type, for all n.

Building on the work of Davenport and Schmidt, we mainly prove two results. The first one is a version of Gel'fond's transcendence criterion which provides a sufficient condition for a complex or p-adic number $\xi$ to be algebraic in terms of the existence of polynomials of bounded degree taking small values at $\xi$ together with most of their derivatives. The second one, which follows from this criterion by an argument of duality, is a result of simultaneous approximation by conjugate algebraic integers for a fixed number $\xi$ that is either transcendental or algebraic of sufficiently large degree. We also present several constructions showing that these results are essentially optimal.

This paper introduces a new graph constructed from a point process. The idea is to connect a point with its nearest neighbour, then to the second nearest and continue this process until the point belongs to the interior of the convex hull of these nearest neighbours. The number of such neighbours is called the degree of a point. We derive the distribution of the degree of the typical point in a Poisson process, prove a central limit theorem for the sum of degrees, and propose an edge-corrected estimator of the distribution of the degree that is unbiased for a stationary Poisson process. Simulation studies show that this degree is a useful concept that allows the separation of clustering and repulsive behaviour of point processes.

The paper shows that specializations of finitely generated graded modules are also graded and that many important invariants of graded modules and ideals are preserved by specializations.

AMS 2000 Mathematics subject classification: Primary 13A02