相关论文: Construction algorithms for plane nets in base $b$

The Weyl operators give a convenient basis of $M_n(\mathbb{C})$ which is also orthonormal with respect to the Hilbert-Schmidt inner product. The properties of such a basis can be generalised to the notion of a nice error basis(NEB), as…

Channel charting builds a map of the radio environment in an unsupervised way. The obtained chart locations can be seen as low-dimensional compressed versions of channel state information that can be used for a wide variety of applications,…

We have developed a general Bayesian algorithm for determining the coordinates of points in a three-dimensional space. The algorithm takes as input a set of probabilistic constraints on the coordinates of the points, and an a priori…

Plane arrangements are a useful tool for surface and volume modelling. However, their main drawback is poor scalability. We introduce two key novelties that enable the construction of plane arrangements for complex objects and entire…

Copi, Huterer, Starkman and Schwarz introduced multipole vectors in a tensor context and used them to demonstrate that the first-year WMAP quadrupole and octopole planes align at roughly the 99.9% confidence level. In the present article…

Multinets are certain configurations of lines and points with multiplicities in the complex projective plane P2. They are used in the studies of resonance and characteristic varieties of complex hyperplane arrangement complements and…

We investigate quasi-Monte Carlo rules for the numerical integration of multivariate periodic functions from Besov spaces $S^r_{p,q}B(\mathbb{T}^d)$ with dominating mixed smoothness $1/p<r<2$. We show that order 2 digital nets achieve the…

In this thesis, a new approach for constructing subdivision algorithms for generalized quadratic and cubic B-spline subdivision for subdivision surfaces and volumes is presented. First, a catalog of quality criteria for these subdivision…

We present algorithms for basic computations with monoids in finitely generated abelian groups such as monoid membership testing and computing an element of the conductor ideal. Applying them to Mori dream spaces, we obtain algorithms to…

We present a framework to define a large class of neural networks for which, by construction, training by gradient flow provably reaches arbitrarily low loss when the number of parameters grows. Distinct from the fixed-space global…

We consider the problem of learning Bayesian networks (BNs) from complete discrete data. This problem of discrete optimisation is formulated as an integer program (IP). We describe the various steps we have taken to allow efficient solving…

We give a Euclidean division algorithm for the real quadratic fields $\mathbb{Q}(\sqrt{m})$ for $m \in \{2, 3, 6, 7, 11, 19\}$, with the property that the norm of the remainder depends on the first Euclidean minimum of the field. In each…

A Bayesian net (BN) is more than a succinct way to encode a probabilistic distribution; it also corresponds to a function used to answer queries. A BN can therefore be evaluated by the accuracy of the answers it returns. Many algorithms for…

High-order difference operators with the summation-by-parts (SBP) property can be used to build stable discretizations of hyperbolic conservation laws; however, most high-order SBP operators require a conforming, high-order mesh for the…

A finite \emph{$k$-net} of order $n$ is an incidence structure consisting of $k\ge 3$ pairwise disjoint classes of lines, each of size $n$, such that every point incident with two lines from distinct classes is incident with exactly one…

We consider geodesic nets (critical points of a length functional on the space of embedded graphs) on doubled polygons (topological 2-spheres endowed with a flat metric away from finitely many cone singularities). We use the theorem of…

We study the complexity of cutting planes and branching schemes from a theoretical point of view. We give some rigorous underpinnings to the empirically observed phenomenon that combining cutting planes and branching into a branch-and-cut…

We present a procedure which allows one to integrate explicitly the class of checkerboard IC-nets which has recently been introduced as a generalisation of incircular (IC) nets. The latter class of privileged congruences of lines in the…

Designing networks with specified collective properties is useful in a variety of application areas, enabling the study of how given properties affect the behavior of network models, the downscaling of empirical networks to workable sizes,…

A variety of scale-free networks have been created since the pioneer work by A.-L. Barab\'{a}si and R. Albert. All this networks are homogeneous since they are composed of the same kind of nodes. In the realistic world, however, one element…