We revisit the problem of integer factorization with number-theoretic oracles, including a well-known problem: can we factor an integer $N$ unconditionally, in deterministic polynomial time, given the value of the Euler totient $(\varphi(N)$? We show that this can be done, under certain size conditions on the prime factors of $N$. The key technique is lattice basis reduction using the LLL algor...

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 provable output quality. One early improvement of the LLL algorithm was LLL with deep insertions (DeepLLL). The output of this version of LLL has higher quality in...

the present study has been conducted on shemiranat county landscape, using lattice hexagon approach, for the first time, in order to achieve homogeneous units in degradation model. to this aim, with respect to the extent of the studied area, a lattice hexagon composed of 36 units (cells) was created and each grid cell was considered as a sub landscape. next, ecological vulnerability, degradatio...

Despite their popularity, lattice reduction algorithms remain mysterious in many ways. It has been widely reported that they behave much more nicely than what was expected from the worst-case proved bounds, both in terms of the running time and the output quality. In this article, we investigate this puzzling statement by trying to model the average case of lattice reduction algorithms, startin...

This letter focuses on solving the challenging problem of detecting natural image boundaries. A boundary usually refers to the border between two regions with different semantic meanings. Therefore, a measurement of dissimilarity between image regions plays a pivotal role in boundary detection of natural images. To improve the performance of boundary detection, a Learning-based Boundary Metric ...

We develop structure-preserving reduced basis methods for a large class of nondissipative problems by resorting to their formulation as Hamiltonian dynamical systems. With this perspective, the phase space is naturally endowed with Poisson manifold structure which encodes physical properties, symmetries, and conservation laws dynamics. The goal design general state-dependent degenerate based on...

In recent years, reduced basis methods (RBMs) have been adapted to the many-body eigenvalue problem and they used, largely in nuclear physics, as fast emulators able bypass expensive direct computations while still providing highly accurate results. This work is meant show that RBM an efficient emulator for strong correlations induced by pairing interaction a variety of finite systems like ultr...

Linear kinetic transport equations play a critical role in optical tomography, radiative transfer and neutron transport. The fundamental difficulty hampering their efficient accurate numerical resolution lies the high dimensionality of physical velocity/angular variables fact that problem is multiscale nature. Leveraging existence hidden low-rank structure hinted by diffusive limit, this work, ...