We exhibit an identity of abstract simplicial complexes between the wellstudied complex of trees Tn and the reduced minimal nested set complex of the partition lattice. We conclude that the order complex of the partition lattice can be obtained from the complex of trees by a sequence of stellar subdivisions. We provide an explicit cohomology basis for the complex of trees that emerges naturally...

Using a new quark-field construction algorithm and a large variational basis of operators, we extract a highly excited isovector meson spectrum on dynamical anisotropic lattices. We show how carefully constructed operators can be used to reliably identify the continuum spin of extracted states, overcoming the reduced cubic symmetry of the lattice. Using this method we extract, with confidence, ...

Abstract: On the basis of the signatures scheme without trapdoors from lattice, which is proposed by Vadim Lyubashevsky in 2012, we present a new ring signature scheme from lattice. The proposed ring signature scheme is an extension of the signatures scheme without trapdoors. We proved that our scheme is strongly unforgeable against adaptive chosen message in the random oracle model, and proved...

We consider Feshbach scattering of fermions in a one-dimensional optical lattice. By formulating the scattering theory in the crystal momentum basis, one can exploit the lattice symmetry and factorize the scattering problem in terms of center-of-mass and relative momentum in the reduced Brillouin zone scheme. Within a single band approximation, we can tune the position of a Feshbach resonance w...

Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 23 October 2020Accepted: 09 September 2021Published online: 04 January 2022Keywordslattice size, reduced lattice basis, polytopeAMS Subject Headings11H06, 52B20, 52C05, 52C07Publication DataISSN (print): 0895-4801ISSN (online): 1095-7146Publisher: Society for Industrial a...

Let B be a basis of a Euclidean lattice, and B̃ an approximation thereof. We give a sufficient condition on the closeness between B̃ and B so that an LLL-reducing transformation U for B̃ remains valid for B. Further, we analyse an efficient reduction algorithm when B is itself a small deformation of an LLL-reduced basis. Applications include speeding-up reduction by keeping only the most significa...

In this paper we present a heuristic based on dynamic approximations for improving the well-known Schnorr-Euchner lattice basis reduction algorithm. In particular, the new heuristic is more efficient in reducing large problem instances and extends the applicability of the Schnorr-Euchner algorithm such that problem instances that the stateof-the-art method fails to reduce can be solved using ou...

In the high-tech world of today, the demand for security is constantly rising. That is why identifying hard computational problems for cryptographical use has become a very important task. It is crucial to find computational problems, which complexity could provide a basis for the security of the cryptosystems. However, there are only very few hard computational problems that are useful for cry...

We present a technique, which we call basis delegation, that allows one to use a short basis of a given lattice to derive a new short basis of a related lattice in a secure way. And since short bases for lattices essentially function like cryptographic trapdoors, basis delegation turns out to be a very powerful primitive. As the main application of our technique, we show how to construct hierar...