We introduce a generalized combinatorial Ricci flow on surfaces of finite topological type. Using a Lyapunov function, we prove that the flow exists for all time and converges to a circle pattern ...metric on surfaces with prescribed curvatures. This suggests an algorithm to find circle patterns on surfaces with obtuse exterior intersection angles. As a comparison, this flow has the advantage of accelerating the convergence rate.
•The C-Circle Assay (CCA) is a rapid, robust and quantitative measure for ALT activity.•Here we detail the protocols and considerations required to perform the CCA.•Including exonuclease removal of ...linear telomeric DNA and synthesis of C-Circle, C96.•The Quick C-Circle Preparation (QCP; a one tube preparation of cells for the CCA).•Modulation of ALT activity by γ-irradiation.
The C-Circle Assay has satisfied the need for a rapid, robust and quantitative ALT assay that responds quickly to changes in ALT activity. The C-Circle Assay involves (i) extraction or simple preparation (Quick C-Circle Preparation) of the cell’s DNA, which includes C-Circles (ii) amplification of the self-primed C-Circles with a rolling circle amplification reaction and (iii) sequence specific detection of the amplification products by native telomeric DNA dot blot or telomeric qPCR. Here we detail the protocols and considerations required to perform the C-Circle Assay and its controls, which include exonuclease removal of linear telomeric DNA, production of the synthetic C-Circle C96 and modulation of ALT activity by γ-irradiation.
This paper aims to introduce a mathematical-philosophical type of question from the fascinating world of generalized circle numbers to the widest possible readership. We start with recalling ...well-known (in part from school) properties of the polygonal approximation of the common circle when approximating the famous circle number π by convergent sequences of upper and lower bounds being based upon the lengths of polygons. Next, we shortly refer to some results from the literature where suitably defined generalized circle numbers of lp- and lp,q-circles, πp and πp,q, respectively, are considered and turn afterwards over to the approximation of an lp-circle by a family of lp,q-circles with q converging to p, q→p. Then we ask whether or not there holds the continuity property πp,q→πpasq→p. The answer to this question leads us to the answer of the question stated in the paper’s title. Presenting here for illustration true paintings instead of strong technical or mathematical drawings intends both to stimulate opening heart and senses of the reader for recognizing generalized circles in his real life and to suggest the philosophical challenge of the consequences coming out from the demonstrated non-continuity property.
Let f and g be two circle endomorphisms of degree d\geq 2 such that each has bounded geometry, preserves the Lebesgue measure, and fixes 1. Let h fixing 1 be the topological conjugacy from f to g. ...That is, h\circ f=g\circ h. We prove that h is a symmetric circle homeomorphism if and only if h=Id.
Blood Flow Distribution in Cerebral Arteries Zarrinkoob, Laleh; Ambarki, Khalid; Wåhlin, Anders ...
Journal of cerebral blood flow and metabolism,
04/2015, Letnik:
35, Številka:
4
Journal Article
Recenzirano
Odprti dostop
High-resolution phase—contrast magnetic resonance imaging can now assess flow in proximal and distal cerebral arteries. The aim of this study was to describe how total cerebral blood flow (tCBF) is ...distributed into the vascular tree with regard to age, sex and anatomic variations. Forty-nine healthy young (mean 25 years) and 45 elderly (mean 71 years) individuals were included. Blood flow rate (BFR) in 21 intra- and extracerebral arteries was measured. Total cerebral blood flow was defined as BFR in the internal carotid plus vertebral arteries and mean cerebral perfusion as tCBF/brain volume. Carotid/vertebral distribution was 72%/28% and was not related to age, sex, or brain volume. Total cerebral blood flow (717±123 mL/min) was distributed to each side as follows: middle cerebral artery (MCA), 21%; distal MCA, 6%; anterior cerebral artery (ACA), 12%, distal ACA, 4%; ophthalmic artery, 2%; posterior cerebral artery (PCA), 8%; and 20% to basilar artery. Deviating distributions were observed in subjects with ‘fetal’ PCA. Blood flow rate in cerebral arteries decreased with increasing age (P<0.05) but not in extracerebral arteries. Mean cerebral perfusion was higher in women (women: 61±8; men: 55±6 mL/min/100 mL, P<0.001). The study describes a new method to outline the flow profile of the cerebral vascular tree, including reference values, and should be used for grading the collateral flow system.
Abstract
Measuring circular shape is a main task of dimensional metrology, characterized by circle diameter and its roundness, both for full circles and circle arcs. Point coordinates allows ...measuring both arcs and full circle, by fitting to substitution geometry, in many cases by least-squares criteria and fitting. Nevertheless, circle shape can be also characterized by the minimum zone, minimum circumscribed and maximum inscribed circles. This research presents a systematic experimental analysis of results of normal distributed points around the substitution circle through simulation, for different circle arc angles to the full circle and for the four mentioned fitting criteria. The results show the influence of arc angle in the variability of the results across criteria and the different behaviour depending on the arc amplitude. The results confirm the good stability and behaviour of least squares and minimum zone criteria, while warns the use of minimum circumscribed and maximum inscribed circles over half circumference. Experimental regression facilitates estimation of the minimum zone criteria from the least squares fitting that are independently verified with literature datasets with good results.
Rolling circle replication (RCR), including rolling circle amplification (RCA) and rolling circle transcription (RCT), is an isothermal enzymatic reaction. Because of its high amplification ...efficiency, RCR is a powerful biosensing tool for detecting biomolecules. In recent years, RCR has also been extended to the field of bioimaging to better understand biological pathways. Furthermore, RCR provides a simple technique to design and generate DNA/RNA structures with unique advantages in delivering drugs and enhanced targeting ability. In this review, we introduce the fundamentals of RCR and describe the most recent advances in RCR-based detection methods and delivery vehicles for biosensing, bioimaging, and biomedicine. Finally, some challenges and further opportunities of RCR-based biotechnology are discussed.
Rolling circle replication (RCR) is an isothermal nucleic acid amplification approach that holds great potential in biotechnology.RCR can serve as a powerful biosensing platform for the detection of various biomolecules in bioanalysis and diagnosis.In bioimaging, RCR can provide a unique perspective in comprehensive understanding of biological processes and effective diagnosis of diseases.Programmable, biodegradable RCR-based assemblies have been used as versatile advanced drug carriers for targeted theranostics.
One of the fundamental methods for shaping the constructional geometry of any building is the use of basic shapes: circles and squares. The circle represents vitality or energy, while the square ...represents strength. In world history, the concept of geometry traces its origins to construction in Egypt and Babylonia, where proportional systems were described through mathematical equations. They later became known as the Pythagorean Theorem, named after Pythagoras. In Ancient India, the concept of geometry starts with the construction of altars for Vedic sacrifices, as per the instructions of the Śulbasūtras. This involved creating circles and squares, converting squares to circles and vice versa, resulting in altars of various shapes and proportionate systems. The intersection of these basic shapes, the square and the circle, is the key to constructional building geometry. For instance, Vesica Piscis is a geometrical element derived from the circle-circle intersection. It has been applied by researchers to examine the geometry of both ancient and modern buildings. Similarly, the Square-Circle Sequence (SCS) is a method derived from the square-circle intersection. Gandotra (2011) used it to study the constructional geometry of the Hindu temples in North India (Nāgara temples). Meister (1985) also applied the square-circle intersection geometric constructional method to define the proportionate system of the Hindu temples in India. Finally, this study attempts to correlate these types of constructional geometry in the evolution of elevational form of Nāgara temples through Lakshman temple in Sirpur. It determines that the building’s elevational form may be derived from the basic shapes of the circle and the square.
Antegrade selective cerebral perfusion (ASCP) with systemic moderate hypothermia is routinely used as brain protection during aortic arch surgery. Whether ASCP should be delivered unilaterally ...(u-ASCP) or bilaterally (bi-ASCP) remains controversial.
We routinely studied the functional anatomy of the circle of Willis (CoW in all patients scheduled for arch surgery using transcranial color-coded Doppler over a decade. On the basis of these data, we classified observed functional variants as being “safe,” “moderately safe,” or “unsafe” for u-ASCP.
From January 2005 to June 2015, 1119 patients underwent aortic arch surgery in our institution. Of these, 636 patients had elective surgery performed with ASCP. Preoperative full functional assessment of the CoW was possible in 61% of patients. A functionally complete CoW was found in only 27%. Of all variants, 72% were classified as being safe for u-ASCP, whereas 18% were moderately safe for u-ASCP, and 10% unsafe. Unsafe variants for bi-ASCP were observed in 0.5% of patients.
The risk of ischemic brain damage due to malperfusion is estimated to be substantially higher during right u-ASCP than during bi-ASCP. Bi-ASCP is therefore highly preferable over u-ASCP if the function of the CoW is unknown. We propose a tailored approach using this full functional assessment preoperatively by applying u-ASCP via the right subclavian artery when considered safely possible, and bi-ASCP when considered a necessity to prevent cerebral malperfusion, and thus thereby try to reduce the embolic stroke risk of ostial instrumentation in bi-ASCP.
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•Circle-to-circle amplification (C2CA) products were affinity-enriched in microfluidics.•C2CA products were measured with both discrete and average signal modes to modulate ...sensitivity.•Microfluidic affinity chromatography enrichment (μACE) detected <1.7 × 103 copies/mL ZIKV RNA.•C2CA-μACE was benchmarked against RT-qPCR providing a Pearson r = 0.95 (discrete signal mode).•C2CA-μACE was demonstrated for ZIKV RNA quantification on in vitro infected PBMCs of healthy donors.
Sensitive viral diagnostic methods are increasingly in demand to tackle emerging epidemics. The Zika virus (ZIKV) is particularly relevant in tropical resource limited settings (RLS) and is associated with intermittent epidemics such as the recent 2016 ZIKV outbreak in South America, wherein Zika fever was classified by WHO as a public health emergency of international concern. Thus, there is an urgent need for widespread Zika fever diagnostics and efficient drug therapies.
ZIKV diagnostics are typically performed using RT-qPCR in centralized laboratories. While extremely sensitive, RT-qPCR requires rapid heating-cooling cycles, combined with continuous fluorescence measurements to allow quantification, implying high costs and limiting availability of molecular diagnostics in RLS. Here, we report isothermal amplification of ZIKV cDNA using padlock probes followed by two rounds of Rolling Circle Amplification (RCA), termed as circle-to-circle amplification (C2CA), combined with a microfluidic affinity chromatography enrichment (μACE) platform. This platform allowed the detection of <17 vRNA copies per reaction mixture, equivalent to ∼3 aM, showed a positive correlation with RT-qPCR in both average (r = 0.80) and discrete (r = 0.95) signal modes, and was validated for drug efficiency tests using in vitro infected peripheral blood mononuclear cells from 3 healthy donors. This performance shows significant promise towards highly sensitive, albeit simple and cost-effective point-of-care viral diagnostics.
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