Axiomatic set theory as a basis for the construction of mathematics

It is widely known that one of the major tasks of 'Foundations' is to construct a formal system which can he said to contain the whole of mathematics. For various reasons axiomatic set theory is a very suitable choice for such a system and it is one which has proved acceptable to both logicians and mathematicians. The particular demands of mathematicians and logicians, however, are not the same. As a result there exist at the moment two different formulations of set theory which can be roughly said to cater for logicians and mathematicians respectively. It is these systems which are the subject of this dissertation. The system of set theory constructed for logicians is by P. Bernays. This will be discussed in chapter II. For mathematicians No Bourbaki has constructed a system of set theory within which he has already embedded a large part of mathematics. This system will be discussed in chapter III. Chapter I is historical and contains some of Cantor's original ideas. The relationship between Bernays' system and (essentially) Bourbaki's system is commented upon in chapter IV. <p

Performance/mathematics: a dramatisation of mathematical methods

This essay conceptualises the notion of performance mathematics in terms of a paradoxical relationship with the constructed notion of truth, which is shared by theatrical and mathematical performance. Specifically, I argue that these two disciplines can and cannot be reconciled with truthfulness. Grounding my comparison on the notion of an axiomatic method common to both disciplines, I argue that theatrical and mathematical performance can speak of truths only when these truths are properly staged or methodologically grounded according to the internal rules and conditions laid out by each discipline. But in the same way that these truths can be constructed, or they can be done, so they can be undone. Arguing that mathematics can be described as a performance of specific outcomes involving abstract objects and functions, I trace a cross-disciplinary comparative analysis of performance elements (especially axioms and functions), drawing on a number of theatre and mathematical theories. Some suggestions are also put forward in terms of the connection between the performance of mathematised texts and computational mathematics, particularly in terms of an inherent poetics and theatricality inside the performance-oriented, mathematised languages of digital computing

In Vivo Detection of Amyloid-β Deposits Using Heavy Chain Antibody Fragments in a Transgenic Mouse Model for Alzheimer's Disease

This study investigated the in vivo properties of two heavy chain antibody fragments (VHH), ni3A and pa2H, to differentially detect vascular or parenchymal amyloid-β deposits characteristic for Alzheimer's disease and cerebral amyloid angiopathy. Blood clearance and biodistribution including brain uptake were assessed by bolus injection of radiolabeled VHH in APP/PS1 mice or wildtype littermates. In addition, in vivo specificity for Aβ was examined in more detail with fluorescently labeled VHH by circumventing the blood-brain barrier via direct application or intracarotid co-injection with mannitol. All VHH showed rapid renal clearance (10–20 min). Twenty-four hours post-injection 99mTc-pa2H resulted in a small yet significant higher cerebral uptake in the APP/PS1 animals. No difference in brain uptake were observed for 99mTc-ni3A or DTPA(111In)-pa2H, which lacked additional peptide tags to investigate further clinical applicability. In vivo specificity for Aβ was confirmed for both fluorescently labeled VHH, where pa2H remained readily detectable for 24 hours or more after injection. Furthermore, both VHH showed affinity for parenchymal and vascular deposits, this in contrast to human tissue, where ni3A specifically targeted only vascular Aβ. Despite a brain uptake that is as yet too low for in vivo imaging, this study provides evidence that VHH detect Aβ deposits in vivo, with high selectivity and favorable in vivo characteristics, making them promising tools for further development as diagnostic agents for the distinctive detection of different Aβ deposits

Computerized clinical decision support systems for drug prescribing and management: A decision-maker-researcher partnership systematic review

<p>Abstract</p> <p>Background</p> <p>Computerized clinical decision support systems (CCDSSs) for drug therapy management are designed to promote safe and effective medication use. Evidence documenting the effectiveness of CCDSSs for improving drug therapy is necessary for informed adoption decisions. The objective of this review was to systematically review randomized controlled trials assessing the effects of CCDSSs for drug therapy management on process of care and patient outcomes. We also sought to identify system and study characteristics that predicted benefit.</p> <p>Methods</p> <p>We conducted a decision-maker-researcher partnership systematic review. We updated our earlier reviews (1998, 2005) by searching MEDLINE, EMBASE, EBM Reviews, Inspec, and other databases, and consulting reference lists through January 2010. Authors of 82% of included studies confirmed or supplemented extracted data. We included only randomized controlled trials that evaluated the effect on process of care or patient outcomes of a CCDSS for drug therapy management compared to care provided without a CCDSS. A study was considered to have a positive effect (<it>i.e.</it>, CCDSS showed improvement) if at least 50% of the relevant study outcomes were statistically significantly positive.</p> <p>Results</p> <p>Sixty-five studies met our inclusion criteria, including 41 new studies since our previous review. Methodological quality was generally high and unchanged with time. CCDSSs improved process of care performance in 37 of the 59 studies assessing this type of outcome (64%, 57% of all studies). Twenty-nine trials assessed patient outcomes, of which six trials (21%, 9% of all trials) reported improvements.</p> <p>Conclusions</p> <p>CCDSSs inconsistently improved process of care measures and seldomly improved patient outcomes. Lack of clear patient benefit and lack of data on harms and costs preclude a recommendation to adopt CCDSSs for drug therapy management.</p