相关论文: Singularity analysis, Hadamard products, and tree …

We adapt algorithms for resolving the singularities of complex algebraic varieties to prove that the natural map of homology theories from complex bordism to the bordism theory of complex derived orbifolds splits. In equivariant stable…

The ensemble inter-relations to be considered are special features of classical cases, where the joint eigenvalue probability density can be computed explicitly. Attention will be focussed too on the consequences of these inter-relations,…

Random forest is widely exploited as an ensemble learning method. In many practical applications, however, there is still a significant challenge to learn from imbalanced data. To alleviate this limitation, we propose a deep dynamic boosted…

We propose methods for density estimation and data synthesis using a novel form of unsupervised random forests. Inspired by generative adversarial networks, we implement a recursive procedure in which trees gradually learn structural…

We develop a symmetry-aware toolkit for finite mixtures whose components are only identifiable up to a finite \emph{folding} group action. The correct estimand is the multiset of parameter orbits in the quotient space, not an ordered list…

Models of disorder with a direction (constant imaginary vector-potential) are considered. These non-Hermitian models can appear as a result of computation for models of statistical physics using transfer matrix technique or describe…

We aim at modelling the appearance of distinct tags in a sequence of labelled objects. Common examples of this type of data include words in a corpus or distinct species in a sample. These sequential discoveries are often summarised via…

For a general formulation of linearised hybrid inverse problems in impedance tomography, the qualitative properties of the solutions are analysed. Using an appropriate scalar pseudo-differential formulation, the problems are shown to permit…

Anomalous diffusion in the presence or absence of an external force field is often modelled in terms of the fractional evolution equations, which can involve the hyper-singular source term. For this case, conventional time stepping methods…

We consider various classes of Motzkin trees as well as lambda-terms for which we derive asymptotic enumeration results. These classes are defined through various restrictions concerning the unary nodes or abstractions, respectively: We…

This chapter collects several probabilistic tools that proved to be useful in the analysis of randomized search heuristics. This includes classic material like Markov, Chebyshev and Chernoff inequalities, but also lesser known topics like…

Ensembles of decision trees are a useful tool for obtaining for obtaining flexible estimates of regression functions. Examples of these methods include gradient boosted decision trees, random forests, and Bayesian CART. Two potential…

Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…

We give first-order asymptotic expansions for the resolvent and Hadamard-type formulas for the eigenvalue curves of one-parameter families of canonically symplectic operators. We allow for parameter dependence in the boundary conditions,…

Simplicial complexes are a popular tool used to model higher-order interactions between elements of complex social and biological systems. In this paper, we study some combinatorial aspects of a class of simplicial complexes created by a…

A computational tool for coarse-graining nonlinear systems of ordinary differential equations in time is discussed. Three illustrative model examples are worked out that demonstrate the range of capability of the method. This includes the…

This is a tutorial on some basic non-asymptotic methods and concepts in random matrix theory. The reader will learn several tools for the analysis of the extreme singular values of random matrices with independent rows or columns. Many of…

I study the product of independent identically distributed $D\times D$ random probability matrices. Some exact asymptotic results are obtained. I find that both the left and the right products approach exponentially to a probability…

Tree structured graphical models are powerful at expressing long range or hierarchical dependency among many variables, and have been widely applied in different areas of computer science and statistics. However, existing methods for…

An analytical method for getting new complex Hadamard matrices by using mutually unbiased bases and a nonlinear doubling formula is provided. The method is illustrated with the n=4 case that leads to a rich family of eight-dimensional…