A forgotten little chapter on isoperimetric inequalities. On the fraction of a convex and closed plane area lying outside a circle with which it shares a diameter

[EN]Often some interesting or simply curious points are left out when developing a theory. It seems that one of them is the existence of an upper bound for the fraction of area of a convex and closed plane area lying outside a circle with which it shares a diameter, a problem stemming from the theory of isoperimetric inequalities. In this paper such a bound is constructed and shown to be attained for a particular area. It is also shown that convexity is a necessary condition in order to avoid the whole area lying outside the circle

Thaumatrope (Magic Circle)

The thaumatrope consists of a circle of cardstock, 2.5 inches in diameter with 2 strings attached, one each at opposite points of the diameter. There were 2 images painted on the cardstock, one on each side, with their positions inverted. The outline of the image was usually printed and the color hand-painted in (Barnes 7).

The E-learning Circle – a holistic software design tool for e-learning

The article introduces the E-learning Circle, a tool developed to assure the quality of the software design process of e-learning systems, considering pedagogical principles as well as technology. The E-learning Circle consists of a number of concentric circles which are divided into three sectors. The content of the inner circles is based on pedagogical principles, while the outer circle specifies how the pedagogical principles may be implemented with technology. The circle’s centre is dedicated to the subject taught, ensuring focus on the specific subject’s properties. The three sectors represent the student, the teacher and the learning objectives. The strengths of the E-learning Circle are the compact presentation combined with the overview it provides, as well as the usefulness of a design tool dealing with complexity, providing a common language and embedding best practice. The E-learning Circle is not a prescriptive method, but is useful in several design models and processes. The article presents two projects where the E-learning Circle was used as a design tool.

Generation of long, fully modified, and serum-resistant oligonucleotides by rolling circle amplification

Rolling Circle Amplification (RCA) is an isothermal enzymatic method generating single-stranded DNA products consisting of concatemers containing multiple copies of the reverse complement of the circular template precursor. Little is known on the compatibility of modified nucleoside triphosphates (dN*TPs) with RCA, which would enable the synthesis of long, fully modified ssDNA sequences. Here, dNTPs modified at any position of the scaffold were shown to be compatible with rolling circle amplification, yielding long (>1 kb), and fully modified single-stranded DNA products. This methodology was applied for the generation of long, cytosine-rich synthetic mimics of telomeric DNA. The resulting modified oligo-nucleotides displayed an improved resistance to fetal bovine serum.

4D/3D reduction of dualities: mirrors on the circle

We engineer a brane picture for the reduction of Seiberg dualities from 4D to 3D, valid also in the presence of orientifold planes. We obtain effective 3D dualities on the circle by T-duality, geometrizing the non-perturbative superpotential which is an affine Toda potential. When reducing to pure 3D, we define a double-scaling limit which creates a sector of interacting singlets, giving a unified mechanism for the brane reduction of dualities.

The Circle: Die neue Kolonisierung des inneren Menschen

Mit Hilfe des zeitgenössischen Romans 'The Circle' von Dave Eggers werden Entgrenzungs- und Verdichtungstendenzen moderner subjektivierter Arbeit illustriert, die einen Zusammenhang mit Burnout- und Erschöpfungsdepressionsdiagnosen plausibilisieren. Angesichts der Uneindeutigkeit der empirischen Evidenz wird vorgeschlagen, die Problematik der modernen Gestalt der Erwerbsarbeit – vor allem für diejenigen am unteren Ende der jeweiligen Hierarchien – nicht nur anhand ihrer Krankheitsträchtigkeit, sondern mit Hilfe des Konzepts der Lebensformen und ihrer normativen Aufladung zu kritisieren: Massiv entgrenzte und verdichtete Arbeit erscheint dann als Bruch des 'Arbeitsversprechens', das sich mit Entstehung der Arbeitsgesellschaft im 19. Jh. herausgebildet hat.

Applicability of the GP Device to the Circle of Willis Arteries by Using a Mathematical Model

According to the World Health Organization, 15 million people suffer stroke worldwide each year, of these, 5 million die and 5 million are permanently disabled. Stroke is therefore a major cause of mortality world-wide. The majority of strokes are caused by a blood clot that occludes an artery in the brain, and although thrombolytic agents such as Alteplase are used to dissolve clots that arise in the arteries of the brain, there are limitations on the use of these thrombolytic agents. However over the past decade, other methods of treatment have been developed which include Thrombectomy Devices e.g. the 'GP' Thrombus Aspiration Device ('GP' TAD). Such devices may be used as an alternative to thrombolytics or in conjunction with them to extract blood clots in arteries such as the middle cerebral artery of the midbrain brain, and the posterior inferior cerebellar artery (PICA) of the posterior aspect of the brain. In this paper, we mathematically model the removal of blood clots using the 'GP' TAD from selected arteries of the brain where blood clots may arise taking into account factors such as the resistances, compliances and inertances effects. Such mathematical modelling may have potential uses in predicting the pressures necessary to extract blood clots of given lengths, and masses from arteries in the Circle of Willis - posterior circulation of the brain

Immunoassays with rolling circle DNA amplification: A versatile platform for ultrasensitive antigen detection

We describe an adaptation of the rolling circle amplification (RCA) reporter system for the detection of protein Ags, termed “immunoRCA.” In immunoRCA, an oligonucleotide primer is covalently attached to an Ab; thus, in the presence of circular DNA, DNA polymerase, and nucleotides, amplification results in a long DNA molecule containing hundreds of copies of the circular DNA sequence that remain attached to the Ab and that can be detected in a variety of ways. Using immunoRCA, analytes were detected at sensitivities exceeding those of conventional enzyme immunoassays in ELISA and microparticle formats. The signal amplification afforded by immunoRCA also enabled immunoassays to be carried out in microspot and microarray formats with exquisite sensitivity. When Ags are present at concentrations down to fM levels, specifically bound Abs can be scored by counting discrete fluorescent signals arising from individual Ag–Ab complexes. Multiplex immunoRCA also was demonstrated by accurately quantifying Ags mixed in different ratios in a two-color, single-molecule-counting assay on a glass slide. ImmunoRCA thus combines high sensitivity and a very wide dynamic range with an unprecedented capability for single molecule detection. This Ag-detection method is of general applicability and is extendable to multiplexed immunoassays that employ a battery of different Abs, each labeled with a unique oligonucleotide primer, that can be discriminated by a color-coded visualization system. ImmunoRCA-profiling based on the simultaneous quantitation of multiple Ags should expand the power of immunoassays by exploiting the increased information content of ratio-based expression analysis.