In this paper, we report that we have solved the shortest vector problem (SVP) over a 128-dimensional lattice, which is currently the highest dimension of the SVP that has ever been solved. The security of lattice-based cryptography is based on the hardness of solving the SVP in lattices. In 2010 Micciancio et al. proposed a Gauss Sieve algorithm for heuristically solving the SVP using list L o...

PURPOSE Recently, the absence of spontaneous venous pulsation (SVP) has been suggested as a vascular risk factor for primary open-angle glaucoma (POAG). As the mechanism behind this phenomenon is still unknown, the authors have studied this vascular component using colour Doppler imaging (CDI). METHODS A total of 236 patients were divided into three diagnostic groups: healthy controls (81), P...

The Shortest Vector Problem (SVP) is the most famous and widely studied computational problem on lattices. Given a lattice L (typically represented by a basis), SVP asks to find the shortest nonzero vector in L. The problem can be defined with respect to any norm, but the Euclidean norm is the most common (see the entry lattice for a definition). A variant of SVP (commonly studied in computatio...

INTRODUCTION Ejaculation is a complex reflex mediated by a spinal ejaculation generator located in the lumbosacral spinal cord and consisting of a population of lumbar spinothalamic (LSt) neurons. LSt neurons and their intraspinal axonal projections contain several neuropeptides, including gastrin-releasing peptide (GRP). AIM To test the hypothesis that GRP is critically involved in mediating...

BACKGROUND Phosphopantetheinyl transferases (PPTases) catalyze the posttranslational modification of carrier proteins by the covalent attachment of the 4'-phosphopantetheine (P-pant) moiety of coenzyme A to a conserved serine residue, a reaction absolutely required for the biosynthesis of natural products including fatty acids, polyketides, and nonribosomal peptides. PPTases have been classifie...

Pharmaceutical companies are manufacturers of both solid and liquid formulations. Solid formulations may be tablets, dry powers, confectionary and solid injectables; liquid formulations may be eye drops, ointments, I.V. and other parenteral solutions. Parenteral solutions are packed as large volume parenteral (LVP) solutions, small volume parenteral (SVP) solutions and dry powders requiring rec...

The worst-case hardness of finding short vectors in ideals of cyclotomic number fields (Ideal-SVP) is a central matter in lattice based cryptography. Assuming the worst-case hardness of Ideal-SVP allows to prove the Ring-LWE and Ring-SIS assumptions, and therefore to prove the security of numerous cryptographic schemes and protocols — including key-exchange, digital signatures, public-key encry...

Purpose To establish a model of the retinal capillary circulation in pigs, which in many aspects is close to the human retina. Methods Using high density confocal microscopy image stacks of immunolabeled porcine retinal whole mounts, microvessels close to the optic nerve head were traced in three dimensions. The direction of flow of individual capillaries was deduced from their arteriolar and...

Minimizing the rank of a matrix subject to affine constraints is a fundamental problem with many important applications in machine learning and statistics. In this paper we propose a simple and fast algorithm SVP (Singular Value Projection) for rank minimization with affine constraints (ARMP) and show that SVP recovers the minimum rank solution for affine constraints that satisfy the restricted...

We show a $$2^{n/2+o(n)}$$ -time algorithm that, given as input basis of lattice $$\mathcal {L}\subset \mathbb {R}^n$$ , finds (non-zero) vector in whose length is at most $$\widetilde{O}(\sqrt{n})\cdot \min \{\lambda _1(\mathcal {L}), \det (\mathcal {L})^{1/n}\}$$ where $$\lambda {L})$$ the shortest non-zero and $$\det determinant. Minkowski showed that {L}) \le \sqrt{n} {L})^{1/n}$$ there exi...