Low Weight Discrete Logarithm and Subset Sum in $$2^{0.65n}$$ with Polynomial Memory

2020 ◽  
pp. 94-122
Author(s):  
Andre Esser ◽  
Alexander May
Keyword(s):  
Discrete Logarithm ◽  
Low Weight ◽  
Subset Sum

scholarly journals A discrete logarithm-based approach to compute low-weight multiples of binary polynomials

2016 ◽  
Vol 38 ◽  
pp. 57-71
Author(s):  
Pietro Peterlongo ◽  
Massimiliano Sala ◽  
Claudia Tinnirello
Keyword(s):  
Discrete Logarithm ◽  
Low Weight

Freeze fracture imaging and computer simulation of liposome structure: Membrane geometry and defects

1983 ◽  
Vol 41 ◽  
pp. 646-647
Author(s):  
Joseph A. Zasadzinski
Keyword(s):  
Liquid Crystalline ◽  
Freeze Fracture ◽  
Continuum Theory ◽  
Closed Surfaces ◽  
Straight Line ◽  
Low Weight ◽  
Concentric Spheres ◽  
Membrane Geometry ◽  
Dupin Cyclides ◽  
Limiting Case

At low weight fractions, many surfactant and biological amphiphiles form dispersions of lamellar liquid crystalline liposomes in water. Amphiphile molecules tend to align themselves in parallel bilayers which are free to bend. Bilayers must form closed surfaces to separate hydrophobic and hydrophilic domains completely. Continuum theory of liquid crystals requires that the constant spacing of bilayer surfaces be maintained except at singularities of no more than line extent. Maxwell demonstrated that only two types of closed surfaces can satisfy this constraint: concentric spheres and Dupin cyclides. Dupin cyclides (Figure 1) are parallel closed surfaces which have a conjugate ellipse (r1) and hyperbola (r2) as singularities in the bilayer spacing. Any straight line drawn from a point on the ellipse to a point on the hyperbola is normal to every surface it intersects (broken lines in Figure 1). A simple example, and limiting case, is a family of concentric tori (Figure 1b).To distinguish between the allowable arrangements, freeze fracture TEM micrographs of representative biological (L-α phosphotidylcholine: L-α PC) and surfactant (sodium heptylnonyl benzenesulfonate: SHBS)liposomes are compared to mathematically derived sections of Dupin cyclides and concentric spheres.

A Novel Approach: Trans-ascending Aorta Balloon Aortic Valvuloplasty via Sternotomy for Treating Severe Valvular Aortic Stenosis in a Low-Weight Infant

2014 ◽  
Vol 17 (1) ◽  
pp. 25 ◽  
Author(s):  
Lei Gao ◽  
Qin Wu ◽  
Xinhua Xu ◽  
Tianli Zhao ◽  
Wancun Jin ◽  
...  
Keyword(s):  
Aortic Stenosis ◽  
Transesophageal Echocardiography ◽  
Severe Aortic Stenosis ◽  
Ascending Aorta ◽  
Balloon Aortic Valvuloplasty ◽  
Congenital Aortic Stenosis ◽  
Novel Approach ◽  
Low Weight ◽  
Aortic Valvuloplasty ◽  
Peak Gradient

<p><b>Background:</b> Severe congenital aortic stenosis in infants is a life-threatening congenital heart anomaly that is typically treated using percutaneous balloon aortic valvuloplasty.</p><p><b>Methods:</b> The usual route is the femoral artery under radiographic guidance. However, this procedure may be limited by the small size of the femoral artery in low-weight infants. An infant weighing only 7 kg with severe aortic stenosis (peak gradient was 103 mmHg) was successfully treated with a novel approach, that is trans-ascending aorta balloon aortic valvuloplasty guided by transesophageal echocardiography.</p><p><b>Results:</b> The patient tolerated the procedure well, and no major complications developed. After the intervention, transesophageal echocardiography indicated a significant reduction of the aortic valvular peak gradient from 103 mmHg to 22 mmHg, no aortic regurgitation was found. Eighteen months after the intervention, echocardiography revealed that the aortic valvular peak gradient had increased to 38 mmHg and that still no aortic regurgitation had occurred.</p><p><b>Conclusions:</b> In our limited experience, trans-ascending aorta balloon aortic valvuloplasty for severe aortic stenosis under transesophageal echocardiography guidance effectively reduces the aortic peak gradient. As this is a new procedure, long-term follow up and management will need to be established. It may be an alternative technique to treat congenital aortic stenosis in low-weight patients.</p>

On generic complexity of the subset sum problem in monoids and groups of integer matrix of order two

2020 ◽  
Vol 25 (4) ◽  
pp. 10-15
Author(s):  
Alexander Nikolaevich Rybalov
Keyword(s):  
Linear Group ◽  
Modular Group ◽  
Special Linear Group ◽  
Second Order ◽  
Integer Matrix ◽  
Subset Sum ◽  
Algorithmic Problems ◽  
Almost All ◽  
Subset Sum Problems ◽  
Generic Complexity

Generic-case approach to algorithmic problems was suggested by A. Miasnikov, I. Kapovich, P. Schupp and V. Shpilrain in 2003. This approach studies behavior of an algo-rithm on typical (almost all) inputs and ignores the rest of inputs. In this paper, we prove that the subset sum problems for the monoid of integer positive unimodular matrices of the second order, the special linear group of the second order, and the modular group are generically solvable in polynomial time.

PERSPECTIVES OF ELLIPTICAL CRYPTOGRAPHY TO ENSURE THE INTEGRITY AND CONFIDENTIALITY OF INFORMATION

2019 ◽  
Author(s):  
Anna ILYENKO ◽  
Sergii ILYENKO ◽  
Yana MASUR
Keyword(s):  
Information Systems ◽  
Elliptic Curve ◽  
Elliptic Curves ◽  
Finite Fields ◽  
Computational Efficiency ◽  
Digital Signature ◽  
Discrete Logarithm ◽  
Algebraic Groups ◽  
Schnorr Signature ◽  
Stability Of Algorithms

In this article, the main problems underlying the current asymmetric crypto algorithms for the formation and verification of electronic-digital signature are considered: problems of factorization of large integers and problems of discrete logarithm. It is noted that for the second problem, it is possible to use algebraic groups of points other than finite fields. The group of points of the elliptical curve, which satisfies all set requirements, looked attractive on this side. Aspects of the application of elliptic curves in cryptography and the possibilities offered by these algebraic groups in terms of computational efficiency and crypto-stability of algorithms were also considered. Information systems using elliptic curves, the keys have a shorter length than the algorithms above the finite fields. Theoretical directions of improvement of procedure of formation and verification of electronic-digital signature with the possibility of ensuring the integrity and confidentiality of information were considered. The proposed method is based on the Schnorr signature algorithm, which allows data to be recovered directly from the signature itself, similarly to RSA-like signature systems, and the amount of recoverable information is variable depending on the information message. As a result, the length of the signature itself, which is equal to the sum of the length of the end field over which the elliptic curve is determined, and the artificial excess redundancy provided to the hidden message was achieved.

Dimeric NGF Mimetic Attenuates Hyperglycaemia and DNA Damage in Mice with Streptozotocin-Induced Early-Stage Diabetes

2020 ◽  
Vol 20 (3) ◽  
pp. 453-463
Author(s):  
Svetlana Yagubova ◽  
Aliy Zhanataev ◽  
Rita Ostrovskaya ◽  
Еlena Anisina ◽  
Тatiana Gudasheva ◽  
...  
Keyword(s):  
Dna Damage ◽  
Comet Assay ◽  
Early Stage ◽  
Alkaline Comet Assay ◽  
Β Cells ◽  
Ghost Cells ◽  
Low Weight

Background: NGF deficiency is one of the reasons for reduced β-cells survival in diabetes. Our previous experiments revealed the ability of low-weight NGF mimetic, GK-2, to reduce hyperglycaemia in a model of advanced diabetes. The increase in DNA damage in advanced diabetes was repeatedly reported, while there were no data about DNA damage in the initial diabetes. Aim: The study aimed to establish whether DNA damage occurs in initial diabetes and whether GK-2 is able to overcome the damage. Methods: The early-stage diabetes was modelled in Balb/c mice by streptozotocin (STZ) (130 mg/kg, i.p.). GK-2 was administered at a dose of 0.5 mg/kg, i.p., subchronically. The evaluation of DNA damage was performed using the alkaline comet assay; the percentage of DNA in the tail (%TDNA) and the percentage of the atypical DNA comets (“ghost cells”) were determined. Results: STZ at this subthreshold dose produced a slight increase in glycemia and MDA. Meanwhile, pronounced DNA damage was observed, concerning mostly the percentage of “ghost cells” in the pancreas, the liver and kidneys. GK-2 attenuated the degree of hyperglycaemia and reduced the % of “ghost cells” and %TDNA in all the organs examined; this effect continued after discontinuation of the therapy. Conclusion: Early-stage diabetes is accompanied by DNA damage, manifested by the increase of “ghost cells” percentage. The severity of these changes significantly exceeds the degree of hyperglycaemia and MDA accumulation. GK-2 exerts an antihyperglycaemic effect and attenuates the degree of DNA damage. Our results indicate that the comet assay is a highly informative method for search of antidiabetic medicines.

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