scholarly journals Recovering the Lattice From Its Random Perturbations

2020 ◽  
Author(s):  
Oren Yakir
Keyword(s):  
Simple Procedure ◽  
Lattice Points ◽  
Random Perturbations ◽  
Random Set ◽  
Gaussian Vector ◽  
Single Realization ◽  
Euclidean Lattice

Abstract Given a $d$-dimensional Euclidean lattice we consider the random set obtained by adding an independent Gaussian vector to each of the lattice points. In this note we provide a simple procedure that recovers the lattice from a single realization of the random set.

Targeting Platelets Containing Electro-encapsulated lloprost to Balloon Injured Aorta in Rats

1995 ◽  
Vol 73 (03) ◽  
pp. 535-542 ◽  
Author(s):  
N Crawford ◽  
A Chajara ◽  
G Pfliegler ◽  
B EI Gamal ◽  
L Brewer ◽  
...  
Keyword(s):  
Time Course ◽  
Therapeutic Potential ◽  
Simple Procedure ◽  
Rat Aorta ◽  
Balloon Injury ◽  
Post Injury ◽  
Antiproliferative Effects ◽  
Platelet Deposition ◽  
Total Dna ◽  
Novel Drug

SummaryDrugs can be electro-encapsulated within platelets and targeted to damaged blood vessels by exploiting the platelet’s natural haemostatic properties to adhere to collagen and other vessel wall constituents revealed by injury. A rat aorta balloon angioplasty model has been used to study the effect on platelet deposition of giving iloprost loaded platelets i.v. during the balloon injury. After labelling the circulating platelets with 111-Indium before balloon injury, time course studies showed maximum platelet deposition on the injured aorta occurred at about 1 h post-injury and the deposition remained stable over the next 2-3 h. When iloprost-loaded platelets were given i.v. during injury and the circulating platelet pool labelled with 111-Indium 30 min later, platelet deposition, measured at 2 h postinjury, was substantially and significantly reduced compared with control platelet treatment. Some antiproliferative effects of iloprost-loaded platelets given i.v. during injury have also been observed. Whereas the incorporation of [3H]-thymidine into aorta intima-media DNA at 3 days post injury was 62-fold higher in balloon injured rats than in control sham operated rats, thymidine incorporation into intima/media of rats which had received iloprost loaded platelets during injury was reduced as compared with rats subjected only to the injury procedure. The reduction was only of near significance, however, but at 14 days after injury the total DNA content of the aorta intima/media of rats given iloprost loaded platelets during injury was significantly reduced. Although iloprost loaded platelets can clearly inhibit excessive platelet deposition, other encapsulated agents may have greater anti-proliferative effects. These studies have shown that drug loaded platelets can be targeted to injured arteries, where they may be retained as depots for local release. We believe this novel drug delivery protocol may have therapeutic potential in reducing the incidence of occlusion and restenosis after angioplasty and thrombolysis treatment. Electro-encapsulation of drugs into platelets is a simple procedure and, using autologous and fully biocompatible and biodegradable platelets as delivery vehicles, might overcome some of the immunological and toxicological problems which have been encountered with other delivery vectors such as liposomes, microbeads, synthetic microcapsules and antibodies.

Visualizing 3D Molecular Structures Using an Augmented Reality App

2019 ◽  
Author(s):  
Kristina Eriksen ◽  
Bjarne Nielsen ◽  
Michael Pittelkow
Keyword(s):  
Augmented Reality ◽  
Small Molecules ◽  
Computer Modelling ◽  
Simple Procedure ◽  
3D Structure ◽  
Molecular Structures ◽  
Free Software ◽  
Programming Skills ◽  
2D Space ◽  
Made In

<p>We present a simple procedure to make an augmented reality app to visualize any 3D chemical model. The molecular structure may be based on data from crystallographic data or from computer modelling. This guide is made in such a way, that no programming skills are needed and the procedure uses free software and is a way to visualize 3D structures that are normally difficult to comprehend in the 2D space of paper. The process can be applied to make 3D representation of any 2D object, and we envisage the app to be useful when visualizing simple stereochemical problems, when presenting a complex 3D structure on a poster presentation or even in audio-visual presentations. The method works for all molecules including small molecules, supramolecular structures, MOFs and biomacromolecules.</p>

Circles on lattices and Hadamard matrices

2019 ◽  
pp. 2-9 ◽  
Author(s):  
N. A. Balonin ◽  
M. B. Sergeev ◽  
J. Seberry ◽  
O. I. Sinitsyna
Keyword(s):  
Hadamard Matrices ◽  
Lattice Points ◽  
Practical Significance ◽  
Upper And Lower Bounds ◽  
Problem Size ◽  
Orthogonal Matrices ◽  
Video Information ◽  
Scientific Schools ◽  
Gauss Theorem ◽  
Triangular Numbers

Introduction: The Hadamard conjecture about the existence of Hadamard matrices in all orders multiple of 4, and the Gauss problem about the number of points in a circle are among the most important turning points in the development of mathematics. They both stimulated the development of scientific schools around the world with an immense amount of works. There are substantiations that these scientific problems are deeply connected. The number of Gaussian points (Z3 lattice points) on a spheroid, cone, paraboloid or parabola, along with their location, determines the number and types of Hadamard matrices.Purpose: Specification of the upper and lower bounds for the number of Gaussian points (with odd coordinates) on a spheroid depending on the problem size, in order to specify the Gauss theorem (about the solvability of quadratic problems in triangular numbers by projections onto the Liouville plane) with estimates for the case of Hadamard matrices. Methods: The authors, in addition to their previous ideas about proving the Hadamard conjecture on the base of a one-to-one correspondence between orthogonal matrices and Gaussian points, propose one more way, using the properties of generalized circles on Z3 .Results: It is proved that for a spheroid, the lower bound of all Gaussian points with odd coordinates is equal to the equator radius R, the upper limit of the points located above the equator is equal to the length of this equator L=2πR, and the total number of points is limited to 2L. Due to the spheroid symmetry in the sector with positive coordinates (octant), this gives the values of R/8 and L/4. Thus, the number of Gaussian points with odd coordinates does not exceed the border perimeter and is no less than the relative share of the sector in the total volume of the figure.Practical significance: Hadamard matrices associated with lattice points have a direct practical significance for noise-resistant coding, compression and masking of video information.

Urease as a Possible Tracer for Sewage Effluent Plumes

1989 ◽  
Vol 21 (2) ◽  
pp. 93-97 ◽  
Author(s):  
R. Sadler
Keyword(s):  
Urease Activity ◽  
Simple Procedure ◽  
Sewage Treatment ◽  
Sewage Treatment Plant ◽  
Treatment Plant ◽  
Particulate Phase ◽  
Untreated Sewage ◽  
Potential Alternative ◽  
Two Parameters ◽  
Point Source Discharges

The suitability of sedimentary urease activity as a potential tracer for sewage outfall plumes has been examined. Enzyme activity is readily measured in the sediments by a relatively simple procedure and results may be obtained within a few hours of sampling. The results of urease measurements in areas around point source discharges were compared with bacteriological data for the same areas. Three areas were selected for study: a discharge of untreated sewage into a harbour, a discharge from a sewage treatment plant to a river and a discharge from a contaminated drain to a small beach. In all cases, positive correlation between the distribution of the two parameters was observed. Urease activity probably reflects the movement of soluble products from the outfall whereas E.coli represents the particulate phase of the discharge. Although further work will be required, urease activity does offer a potential alternative to E.coli for tracing plumes of faecal pollution.

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