Related papers: Predicting Module-Lattice Reduction
Lattice reduction is a combinatorial optimization problem aimed at finding the most orthogonal basis in a given lattice. The Lenstra-Lenstra-Lov\'asz (LLL) algorithm is the best algorithm in the literature for solving this problem. In light…
Lattice reduction (LR) aided multiple-input-multiple-out (MIMO) linear detection can achieve the maximum receive diversity of the maximum likelihood detection (MLD). By emloying the most commonly used Lenstra, Lenstra, and L. Lovasz (LLL)…
Lattice reduction algorithms have numerous applications in number theory, algebra, as well as in cryptanalysis. The most famous algorithm for lattice reduction is the LLL algorithm. In polynomial time it computes a reduced basis with…
Lattice reduction algorithms, such as the LLL algorithm, have been proposed as preprocessing tools in order to enhance the performance of suboptimal receivers in MIMO communications. In this paper we introduce a new kind of lattice…
We obtain an exact analytic expression for the quasinormal modes of a noncommutative massless scalar field in the background of a massive spinless BTZ black hole up to the first order in the deformation parameter. We also show that the…
Lattice Boltzmann (LB) on quantum devices must reconcile unitary gate evolution with the dissipative \emph{collision} step. In the multiple-relaxation-time (MRT) class, we work in the common setting of \emph{modewise diagonal} moment…
The current status of the lattice-QCD calculations of the form factors of the $B\to D^\ast\ell\nu$ semileptonic decay is reviewed. Particular emphasis is given to the most mature calculation at non-zero recoil coming from the Fermilab…
Bubeck and Sellke (2021) pose as an open problem the connection between the law of robustness and robust generalization. The law of robustness states that overparameterization is necessary for models to interpolate robustly; in particular,…
With the advancement of blockchain systems, many recent research works have proposed distributed ledger technology~(DLT) that employs Byzantine fault-tolerant~(BFT) consensus protocols to decide which block to append next to the ledger.…
Recently in the Wien2k code, the modified Becke-Johnson potential (mBJLDA) was implemented. As the authors [{\em Phys.Rev.Lett.} 102, 226401 (2009)] point, this potential reproduces the band gap of semiconductors with improved accuracy. In…
The theta series of a lattice is a power series that characterizes the number of lattice vectors at certain norms. It is closely related to a critical quantity widely used in physical layer security and cryptography, known as the flatness…
In recent years, a variety of gradient-based first-order methods have been developed to solve bi-level optimization problems for learning applications. However, theoretical guarantees of these existing approaches heavily rely on the…
We consider connections between similar sublattices and coincidence site lattices (CSLs), and more generally between similar submodules and coincidence site modules of general (free) $\mathbb{Z}$-modules in $\mathbb{R}^d$. In particular, we…
Bivariate bicycle (BB) codes are a prominent class of quantum LDPC codes constructed from group algebras. While the logical dimension and quantum distance of \emph{coprime} BB codes are known to be determined by a greatest common divisor…
Language Models (LLMs) are often quantized to lower precision to reduce the memory cost and latency in inference. However, quantization often degrades model performance, thus fine-tuning is required for various down-stream tasks.…
The Korkine--Zolotareff (KZ) reduction, and its generalisations, are widely used lattice reduction strategies in communications and cryptography. The KZ constant and Schnorr's constant were defined by Schnorr in 1987. The KZ constant can be…
The present work is dedicated to a better understanding of the stability properties of regularized lattice Boltzmann (LB) schemes. To this extent, linear stability analyses of two-dimensional models are proposed: the standard…
As a typical application, the Lenstra-Lenstra-Lovasz lattice basis reduction algorithm (LLL) is used to compute a reduced basis of the orthogonal lattice for a given integer matrix, via reducing a special kind of lattice bases. With such…
PBZ*-lattices are algebraic structures related to quantum logics, which consist of bounded lattices endowed with two kinds of complements, named {\em Kleene} and {\em Brouwer}, such that the Kleene complement satisfies a weakening of the…
To build a fault-tolerant quantum computer, it is necessary to implement a quantum error correcting code. Such codes rely on the ability to extract information about the quantum error syndrome while not destroying the quantum information…