Around the Van Daele–Schmüdgen Theorem

For a {bounded} non-negative self-adjoint operator acting in a complex, infinite-dimensional, separable Hilbert space H and possessing a dense range R we propose a new approach to characterisation of phenomenon concerning the existence of subspaces M\subset H such that M\capR=M^\perp\capR=\{0\}. We show how the existence of such subspaces leads to various {pathological} properties of {unbounded} self-adjoint operators related to von Neumann theorems \cite{Neumann}--\cite{Neumann2}. We revise the von Neumann-Van Daele-Schm\"udgen assertions \cite{Neumann}, \cite{Daele}, \cite{schmud} to refine them. We also develop {a new systematic approach, which allows to construct for any {unbounded} densely defined symmetric/self-adjoint operator T infinitely many pairs of its closed densely defined restrictions T_k\subset T such that \dom(T^* T_{k})=\{0\} (\Rightarrow \dom T_{k}^2=\{0\}$) k=1,2 and \dom T_1\cap\dom T_2=\{0\}, \dom T_1\dot+\dom T_2=\dom T

Introduction to representations of the canonical commutation and anticommutation relations

Lecture notes of a minicourse given at the Summer School on Large Coulomb Systems - QED in Nordfjordeid, 2003, devoted to representations of the CCR and CAR. Quasifree states, the Araki-Woods and Araki-Wyss representations, and the lattice of von Neumenn algebras in a bosonic/fermionic Fock space are discussed in detail

Demographic, clinical and antibody characteristics of patients with digital ulcers in systemic sclerosis: data from the DUO Registry

OBJECTIVES: The Digital Ulcers Outcome (DUO) Registry was designed to describe the clinical and antibody characteristics, disease course and outcomes of patients with digital ulcers associated with systemic sclerosis (SSc). METHODS: The DUO Registry is a European, prospective, multicentre, observational, registry of SSc patients with ongoing digital ulcer disease, irrespective of treatment regimen. Data collected included demographics, SSc duration, SSc subset, internal organ manifestations, autoantibodies, previous and ongoing interventions and complications related to digital ulcers. RESULTS: Up to 19 November 2010 a total of 2439 patients had enrolled into the registry. Most were classified as either limited cutaneous SSc (lcSSc; 52.2%) or diffuse cutaneous SSc (dcSSc; 36.9%). Digital ulcers developed earlier in patients with dcSSc compared with lcSSc. Almost all patients (95.7%) tested positive for antinuclear antibodies, 45.2% for anti-scleroderma-70 and 43.6% for anticentromere antibodies (ACA). The first digital ulcer in the anti-scleroderma-70-positive patient cohort occurred approximately 5 years earlier than the ACA-positive patient group. CONCLUSIONS: This study provides data from a large cohort of SSc patients with a history of digital ulcers. The early occurrence and high frequency of digital ulcer complications are especially seen in patients with dcSSc and/or anti-scleroderma-70 antibodies

The importance of the altricial – precocial spectrum for social complexity in mammals and birds:A review

Various types of long-term stable relationships that individuals uphold, including cooperation and competition between group members, define social complexity in vertebrates. Numerous life history, physiological and cognitive traits have been shown to affect, or to be affected by, such social relationships. As such, differences in developmental modes, i.e. the ‘altricial-precocial’ spectrum, may play an important role in understanding the interspecific variation in occurrence of social interactions, but to what extent this is the case is unclear because the role of the developmental mode has not been studied directly in across-species studies of sociality. In other words, although there are studies on the effects of developmental mode on brain size, on the effects of brain size on cognition, and on the effects of cognition on social complexity, there are no studies directly investigating the link between developmental mode and social complexity. This is surprising because developmental differences play a significant role in the evolution of, for example, brain size, which is in turn considered an essential building block with respect to social complexity. Here, we compiled an overview of studies on various aspects of the complexity of social systems in altricial and precocial mammals and birds. Although systematic studies are scarce and do not allow for a quantitative comparison, we show that several forms of social relationships and cognitive abilities occur in species along the entire developmental spectrum. Based on the existing evidence it seems that differences in developmental modes play a minor role in whether or not individuals or species are able to meet the cognitive capabilities and requirements for maintaining complex social relationships. Given the scarcity of comparative studies and potential subtle differences, however, we suggest that future studies should consider developmental differences to determine whether our finding is general or whether some of the vast variation in social complexity across species can be explained by developmental mode. This would allow a more detailed assessment of the relative importance of developmental mode in the evolution of vertebrate social systems

Radical Constructivism and Radical Constructedness: Luhmann’s Sociology and the Non-linear Dynamics of Expectations

The communication (and reflexive translation) of denotations between semantic domains can generate “horizons of meaning” as reflexive orders that remain structurally coupled to individual minds. Luhmann noted that this elusive order contains a trade-off between “organization” at interfaces integrating (differently coded) expectations at each moment of time, and the potential of further differentiation among symbolically generalized codes of communication in a “self-organization” over time. One can model the coding in the communication of meaning as eigenvectors which evolve as an implication of the interacting intentions and expectations. The interacting horizons of meaning generate new options (redundancy) against the arrow of time, since meaning is provided to events from the perspective of hindsight. Using the theory and computation of anticipatory systems, “self-organization” and “interaction” can be considered as hyper-incursive routines that use (expectations of) future states for their reconstruction, whereas “organization” operates in terms of instantiations (of expectations). Mathematical metaphors can guide us in further exploring the nonlinear dynamics of a social order of intentions and expectations without reification

Science as an Agent of Change: Finalization and Experimental Implementation

Krohn W, van den Daele W. Science as an Agent of Change: Finalization and Experimental Implementation. Social Science Information. 1998;37(1):191-222

European Biotechnology Regulation: Framing the Risk Assessment of a Herbicide-Tolerant Crop

As products of the "new biotechnology," genetically modified organisms have provoked a wide-ranging risk debate on potential harm, especially from herbicide-tolerant crops. In response to this legitimacy problem, the European Community adopted precautionary legislation, which left open the definition of environmental harm. When the U.K. proposed Europe-wide market approval of a herbicide-tolerant oilseed rape (canola), the proposal encountered dissent from some countries and environmentalisi groups. Further debate on normative judgments became necessary to implement the precaution- ary legislation. In dispute were several regulatory boundaries-of administrative re- sponsibility, causality, acceptability, and evidence. The boundary disputes expressed divergent framings of biotechnological risk, each with its implicit model of the socionatu- ral order In this way, the disputes can illuminate the sorts of risk framings that have already become embedded and standardized in other regulatory sectors