Related papers: Normaliz 2013-2016
In this paper, we introduce a decomposition lemma that allows error terms to be expressed using fewer rank-one symmetric matrices than $\frac{n(n+1)}{2}$ within the convex integration scheme of constructing flexible $C^{1,\alpha}$ solutions…
In recent years, techniques based on convex optimization and real algebra that produce converging hierarchies of lower bounds for polynomial minimization problems have gained much popularity. At their heart, these hierarchies rely crucially…
Over the past few years there has been considerable progress in the structural understanding of special Colombeau algebras. We present some of the main trends in this development: non-smooth differential geometry, locally convex theory of…
An extension of dimensional regularization to the case of compact dimensions is presented. The procedure preserves the Kaluza-Klein tower structure, but has a regulator specific to the compact dimension. Possible 5 and 4 dimensional…
In this paper, the regularization approach introduced recently for nonparametric estimation of linear systems is extended to the estimation of nonlinear systems modelled as Volterra series. The kernels of order higher than one, representing…
We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…
For a nonempty polyhedral set $P\subset \mathbb R^d$, let $\mathcal F(P)$ denote the set of faces of $P$, and let $N(P,F)$ be the normal cone of $P$ at the nonempty face $F\in\mathcal F(P)$. We prove that the function $\sum_{F\in\mathcal…
New methods for $D$-decomposition analysis are presented. They are based on topology of real algebraic varieties and computational real algebraic geometry. The estimate of number of root invariant regions for polynomial parametric families…
Regularization methods are a key tool in the solution of inverse problems. They are used to introduce prior knowledge and make the approximation of ill-posed (pseudo-)inverses feasible. In the last two decades interest has shifted from…
We describe a method for constructing characters of combinatorial Hopf algebras by means of integrals over certain polyhedral cones. This is based on ideas from resurgence theory, in particular on the construction of well-behaved averages…
In 1965 Dag Prawitz presented an extension of Gentzen-type systems of Natural Deduction to modal concepts of S4. Maria da Paz Medeiros showed in 2006 that the proof of normalisation for classical S4 does not hold and proposed a new proof of…
Motivated by the analysis of the performance of the simplex method we study the behavior of families of pivot rules of linear programs. We introduce normalized-weight pivot rules which are fundamental for the following reasons: First, they…
We give a type system in which the universe of types is closed by reflection into it of the logical relation defined externally by induction on the structure of types. This contribution is placed in the context of the search for a natural,…
The authors are doing the readers of Statistical Science a true service with a well-written and up-to-date overview of boosting that originated with the seminal algorithms of Freund and Schapire. Equally, we are grateful for high-level…
This paper develops a geometric framework for the stability analysis of differential inclusions governed by maximally monotone operators. A key structural decomposition expresses the operator as the sum of a convexified limit mapping and a…
This paper gives additional background in algebraic geometry as an accompaniment to the article, ``Formal Groups, Elliptic Curves, and some Theorems of Couveignes'' [arXiv:math.NT/9708215]. Section 1 discusses the addition law on elliptic…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
We strengthen the standard bifurcation theorems for saddle-node, transcritical, pitchfork, and period-doubling bifurcations of maps. Our new formulation involves adding one or two extra terms to the standard truncated normal forms with…
We investigate modified steepest descent methods coupled with a loping Kaczmarz strategy for obtaining stable solutions of nonlinear systems of ill-posed operator equations. We show that the proposed method is a convergent regularization…
A new general decomposition theory inspired from modular graph decomposition is presented. This helps unifying modular decomposition on different structures, including (but not restricted to) graphs. Moreover, even in the case of graphs,…