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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Solving hidden number problem with lattice sieving
晶格筛分 隐数问题 格约简算法
2023/4/28
Lattice reduction algorithms have been proved to be one of the most powerful and versatile tools in public key cryptanalysis. In this talk, we primarily concentrate on lattice attacks against (EC)DSA ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Algebro-geometric solutions to the Bogoyavlensky lattice 2(3) equations
博戈亚夫连斯基格2（3）方程 代数几何解 四边形曲线理论
2023/5/5
The theory of tetragonal curves is established and first applied to the study of algebro-geometric quasi-periodic solutions of discrete soliton equations. Using the zero-curvature equation and the dis...
The main model studied in this paper is a lattice of pendula with a nearestneighbor coupling. If the coupling isweak, then the system is near-integrable and KAM tori fill most of the phase space. For ...
ROTOR-ROUTER AGGREGATION ON THE LAYERED SQUARE LATTICE
ROTOR-ROUTER AGGREGATION LAYERED SQUARE LATTICE
2015/8/14
In rotor-router aggregation on the square lattice Z2, particles starting at the origin perform deterministic analogues of random walks until reaching an unoccupied site. The limiting shape of the clus...
Asymptotics of the solutions of the stochastic lattice wave equation
solutions stochastic lattice wave equation
2015/7/14
We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-...
3D integrable lattice models and the Bazhanov-Stroganov model
3D integrable lattice models Bazhanov-Stroganov model
2015/3/19
Many 2D integrable lattice spin models known: Ising, XXZ, RSOS, etc.Systematic construction of solutions of Y-B equations: quantum groups.Not many integrable 3D models: almost all generalizations of Z...
Exact Solutions to the Six-Vertex Model with Domain Wall Boundary Conditions and Uniform Asymptotics of Discrete Orthogonal Polynomials on an Infinite Lattice
Statistical Mechanics Random Matrices Orthogonal Polynomials Asymptotics Riemann-Hilbert Problems
2015/1/19
In this dissertation the partition function, $Z_n$, for the six-vertex model with domain wall boundary conditions is solved in the thermodynamic limit in various regions of the phase diagram. In the f...
USING LATTICE TOPOLOGY INFORMATION TO INVESTIGATE PERSISTENT SCATTERERS AT FACADES IN URBAN AREAS
High resolution SAR Urban Pattern Data Fusion
2014/4/24
Modern spaceborne SAR sensors like TerraSAR-X offer ground resolution of up to one meter in range and azimuth direction. Buildings, roads, bridges, and other man-made structures appear in such data of...
Integrable semi-discretizations and full-discretization of the two dimensional Leznov lattice
Integrable system Integrable discretization cklund transformation Lax pair
2012/8/8
In this paper, semi-discretizations and full-discretization of the Leznov lattice are investigated via
Hirota's bilinear formalism. As a result, two integrable semi-discrete versions and one fully di...
Lattice-point generating functions for free sums of convex sets
Lattice-point generating functions free sums of convex sets Combinatorics
2012/7/11
Let $\J$ and $\K$ be convex sets in $\R^{n}$ whose affine spans intersect at a single rational point in $\J \cap \K$, and let $\J \oplus \K = \conv(\J \cup \K)$. We give expressions for the generating...
A spectral sequence on lattice homology
Lattice homology Heegaard Floer homology spectral sequence
2012/6/29
Using the link surgery formula for Heegaard Floer homology we find a spectral sequence from the lattice homology of a plumbing tree to the Heegaard Floer homology of the corresponding 3-manifold. This...
Average Number of Lattice Points in a Disk
lattice points Weyl asymptotics Bessel function
2012/6/29
The difference between the number of lattice points in a disk of radius $\sqrt{t}/2\pi$ and the area of the disk $t/4\pi$ is equal to the error in the Weyl asymptotic estimate for the eigenvalue count...
Lattice Point Generating Functions and Symmetric Cones
Lattice Point Generating Functions Symmetric Cones Combinatorics
2012/6/29
We show that a recent identity of Beck-Gessel-Lee-Savage on the generating function of symmetrically contrained compositions of integers generalizes naturally to a family of convex polyhedral cones th...
Local statistics of lattice points on the sphere
Local statistics lattice points sphere Number Theory
2012/4/17
We study the spatial distribution of the representation of a large integer as a sum of three squares, on the small and critical scale as well as their electrostatic energy. The main results announced ...
Lattice multi-polygons
Lattice polygon twelve-point theorem Pick’s formula Ehrhart polynomial toric topology
2012/4/17
We discuss generalizations of some results on lattice polygons to certain piecewise linear loops which may have a self-intersection but have vertices in the lattice $\Z^2$. We first prove a formula on...