Author name cluster

Alexander Kurz

Possible papers associated with this exact author name in Arrow. This page groups case-insensitive exact name matches and is not a full identity disambiguation profile.

10 papers

1 author row

YNICL Journal 2014 Journal Article

LRP-1 polymorphism is associated with global and regional amyloid load in Alzheimer's disease in humans in-vivo

Timo Grimmer
Oliver Goldhardt
Liang-Hao Guo
Behrooz H. Yousefi
Stefan Förster
Alexander Drzezga
Christian Sorg
Panagiotis Alexopoulos

OBJECTIVE: Impaired amyloid clearance has been proposed to contribute to β-amyloid deposition in sporadic late-onset Alzheimer's disease (AD). Low density lipoprotein receptor-related protein 1 (LRP-1) is involved in the active outward transport of β-amyloid across the blood-brain barrier (BBB). The C667T polymorphism (rs1799986) of the LRP-1 gene has been inconsistently associated with AD in genetic studies. We aimed to elucidate the association of this polymorphism with in-vivo brain amyloid load of AD patients using amyloid PET with [(11)C]PiB. MATERIALS AND METHODS: 72 patients with very mild to moderate AD were examined with amyloid PET and C667T polymorphism was obtained using TaqMan PCR assays. The association of C667T polymorphism with global and regional amyloid load was calculated using linear regression and voxel based analysis, respectively. The effect of the previously identified modulator of amyloid uptake, the apolipoprotein E genotype, on this association was also determined. RESULTS: The regression analysis between amyloid load and C667T polymorphism was statistically significant (p = 0.046, β = 0.236). In an additional analysis ApoE genotype and gender were identified to explain further variability of amyloid load. Voxel based analysis revealed a significant (p < 0.05) association between C667T polymorphism and amyloid uptake in the temporo-parietal cortex bilaterally. ApoE did not interact significantly with the LRP-1 polymorphism. DISCUSSION: In conclusion, C667T polymorphism of LRP-1 is moderately but significantly associated with global and regional amyloid deposition in AD. The relationship appears to be independent of the ApoE genotype. This finding is compatible with the hypothesis that impaired amyloid clearance contributes to amyloid deposition in late-onset sporadic AD.

Details DOI

Highlights Conference 2013 Conference Abstract

On regular expressions and nominal automata

Alexander Kurz
Tomoyuki Suzuki
Emilio Tuosto

In several branches of computer sciences, automata are often used to describe computational behaviours. Among those developments, automata equipped with resource devices, e. g. a finite-memory or local registers, and languages over infinite alphabets are collecting more and more attentions. In this talk, we would like to discuss a possible general theory for those resource-handling automata from the point of nominal regular expressions. As already published works, we shall present the laywered-technique and the Kleene-style theorem. On top, as our ongoing work, by comparing possible actions (labels) on transitions, we will provide how those actions differentiate their language-recognisability and show the automata-hierarchy of languages over infinite alphabets.

PDF Details

YNIMG Journal 2013 Journal Article

Selectively and progressively disrupted structural connectivity of functional brain networks in Alzheimer's disease — Revealed by a novel framework to analyze edge distributions of networks detecting disruptions with strong statistical evidence

Klaus Hahn
Nicholas Myers
Sergei Prigarin
Karsten Rodenacker
Alexander Kurz
Hans Förstl
Claus Zimmer
Afra M. Wohlschläger

Alzheimer's disease (AD) disrupts selectively and progressively (increasing with severity) functional connectivity of intrinsic brain networks (IBNs), most prominent in the default mode network. Given that IBNs' functional connectivity depends on structural connectivity, we hypothesize for our study selective and progressive changes of IBN based structural connectivity in AD. To achieve strong statistical evidence, we introduce a novel statistical method based on the edge frequency distributions of structural connectivity networks. Such non-Gaussian distributions are compared in a multiple testing scheme, combining a flexible nonparametric test statistic with permutation based strong control of the family wise error rate. We assessed 26 healthy elderly, 23 patients with AD-dementia, and 28 patients with mild cognitive impairment (MCI) by resting-state functional MRI, diffusion tensor imaging, and clinical–neuropsychological testing including annual follow-up assessment. After 3years, 50% of the patients with MCI converted to AD. Tractography of diffusion tensor data identifies structural connectivity networks between regions of IBNs, which are detected by an independent component analysis of resting state fMRI data. We find that IBNs' structural connectivity is selectively and progressively disrupted with primary changes in the default mode network. Correspondent results are found for IBNs' functional connectivity. In addition, structural connectivity across the nodes of all IBNs separated individual MCI patients converting to AD from non-converters. Conclusively, our study provides a new approach to analyze connectivity networks by their non-Gaussian edge frequency distributions and achieves strong statistical evidence by application of the family wise error rate. Data analysis provides selective and progressive disruptions of IBN's structural connectivity in AD and demonstrates the increased power of our method compared to recent studies.

Details DOI

TCS Journal 2012 Journal Article

Modalities in the Stone age: A comparison of coalgebraic logics

Alexander Kurz
Raul Leal

Coalgebra develops a general theory of transition systems, parametric in a functor T; the functor T specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T, a logic for T -coalgebras. We compare two existing proposals, Moss’s coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in Raul Andres Leal (2008) [34] by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatisation of Moss’s logic. The three logics are equivalent for a natural but restricted class of functors. We give examples showing that the logics differ in general. Finally, we argue that the quest for a generic logic for T -coalgebras is still open in the general case.

Details DOI

I&C Journal 2010 Journal Article

Presenting functors on many-sorted varieties and applications

Alexander Kurz
Daniela Petrişan

This paper studies several applications of the notion of a presentation of a functor by operations and equations. We show that the technically straightforward generalisation of this notion from the one-sorted to the many-sorted case has several interesting consequences. First, it can be applied to give equational logic for the binding algebras modelling abstract syntax. Second, it provides a categorical approach to algebraic semantics of first-order logic. Third, this notion links the uniform treatment of logics for coalgebras of an arbitrary type T with concrete syntax and proof systems. Analysing the many-sorted case is essential for modular completeness proofs of coalgebraic logics.

Details DOI

YNIMG Journal 2008 Journal Article

Multivariate and univariate neuroimaging biomarkers of Alzheimer's disease

Christian Habeck
Norman L. Foster
Robert Perneczky
Alexander Kurz
Panagiotis Alexopoulos
Robert A. Koeppe
Alexander Drzezga
Yaakov Stern

We performed univariate and multivariate discriminant analysis of FDG–PET scans to evaluate their ability to identify Alzheimer's disease (AD). FDG–PET scans came from two sources: 17 AD patients and 33 healthy elderly controls were scanned at the University of Michigan; 102 early AD patients and 20 healthy elderly controls were scanned at the Technical University of Munich, Germany. We selected a derivation sample of 20 AD patients and 20 healthy controls matched on age with the remainder divided into 5 replication samples. The sensitivity and specificity of diagnostic AD-markers and threshold criteria from the derivation sample were determined in the replication samples. Although both univariate and multivariate analyses produced markers with high classification accuracy in the derivation sample, the multivariate marker's diagnostic performance in the replication samples was superior. Further, supplementary analysis showed its performance to be unaffected by the loss of key regions. Multivariate measures of AD utilize the covariance structure of imaging data and provide complementary, clinically relevant information that may be superior to univariate measures.

Details DOI

TCS Journal 2004 Journal Article

Stone coalgebras

Clemens Kupke
Alexander Kurz
Yde Venema

We argue that the category of Stone spaces forms an interesting base category for coalgebras, in particular, if one considers the Vietoris functor as an analogue to the power set functor on the category of sets. We prove that the so-called descriptive general frames, which play a fundamental role in the semantics of modal logics, can be seen as Stone coalgebras in a natural way. This yields a duality between modal algebras and coalgebras for the Vietoris functor. Building on this idea, we introduce the notion of a Vietoris polynomial functor over the category of Stone spaces. For each such functor T we provide an adjunction between T-sorted Boolean algebras with operators and the Stone coalgebras for T. We also identify the subcategory of algebras on which the adjunction restricts to an equivalence and show that the final T-coalgebra is the dual of the initial T-BAO.

Details DOI

TCS Journal 2003 Journal Article

Observational logic, constructor-based logic, and their duality

Michel Bidoit
Rolf Hennicker
Alexander Kurz

Observability and reachability are important concepts for formal software development. While observability concepts are used to specify the required observable behavior of a program or system, reachability concepts are used to describe the underlying data in terms of datatype constructors. In this paper we first reconsider the observational logic institution which provides a logical framework for dealing with observability. Then we develop in a completely analogous way the constructor-based logic institution which formalizes a novel treatment of reachability. Both institutions are tailored to capture the semantically correct realizations of a specification from either the observational or the reachability point of view. We show that there is a methodological and even formal duality between both frameworks. In particular, we establish a correspondence between observer operations and datatype constructors, observational and constructor-based algebras, fully abstract and reachable algebras, and observational and inductive consequences of specifications. The formal duality between the observability and reachability concepts is established in a category-theoretic setting.

Details DOI

TCS Journal 2002 Journal Article

On institutions for modular coalgebraic specifications

Alexander Kurz
Rolf Hennicker

We present an algebraic extension of standard coalgebraic specification techniques for state-based systems which allows us to integrate constants and n-ary operations in a smooth way and which leads to institutions enabling the use of modular specification techniques. A sound and complete proof system for first-order observational properties of modular specifications is given. The framework of (Ω, Ξ)-structures that we present can be considered as the result of a transformation of concepts of observational logic as in Hennicker and Bidoit (in: A. Haeberer (Ed.), Algebraic Methodology and Software Technology (AMAST’98), Lecture Notes in Computer Science, vol. 1548, Springer, Berlin, 1999) into the coalgebraic world. Moreover, it is shown that the features of (Ω, Ξ)-structures that make them suitable models for an observational approach to specifications can be categorically expressed by the fact that the operation mapping an (Ω, Ξ)-structure to its behaviour is a fibred idempotent monad.

Details DOI

TCS Journal 2001 Journal Article

Specifying coalgebras with modal logic

Alexander Kurz

We propose to use modal logic as a logic for coalgebras and discuss it in view of the work done on coalgebras as a semantics of object-oriented programming. Two approaches are taken: First, standard concepts of modal logic are applied to coalgebras. For a certain kind of functor it is shown that the logic exactly captures the notion of bisimulation and a complete calculus is given. Examples of verifications of object properties are given. Second, we discuss the relationship of this approach with the coalgebraic logic of Moss (Coalgebraic logic, Ann Pure Appl. Logic 96 (1999) 277–317.).

Details DOI